George M. Bergman -- publications and preprints

Books

• An Invitation to General Algebra and Universal Constructions, 2015, Springer Universitext, x+572 pp.  DOI,  ISBN9 78-3-319-11477-4,  eBook ISBN 978-3-319-11478-1.  MR3309721 . Google Books view. 
  (First edition: ISBN 0-9655211-4-1, published by Henry Helson, 1998  MR1650275 .)

• Cogroups and Co-rings in Categories of Associative Rings (with Adam O. Hausknecht), A.M.S. Math. Surveys and Monographs, v.45, ix+388 pp., 1996; ISBN 0-8218-0495-2.  MR1387111.  Google Books view.  errata and updates. 

     I also have a page of notes on posting to the arXiv, and one offering variants of the LaTeX commands \langle and \rangle. 

     Links below to preprints and recent reprints are set up so that depending on which part of the title you click on, you get the TeX source file, or one or more of PS, DVI, or PDF versions.  You can tell which by moving your cursor along the title, and watching the suffix on the URL at the bottom of your browser screen change. 

Unpublished notes:  These are listed on a page of their own.

Preprints

• On semigroups that are prime in the sense of Tarski, and groups prime in the senses of Tarski and of Rhodes, 17 pp., last revised Oct. 17, 2024.  arXiv:2409.15541.  abstract. 
• Some frustrating questions on dimensions of products of posets, 12 pp.; last revised Feb. 11, 2024.  arXiv:2312.12615.  abstract. 

Published papers

• An elementary result on infinite and finite direct sums of modules,,  J.Alg., 631 (2023) 731-737.  arXiv:2208.06511. abstract.  MR4594881. 
• A type of algebraic structure related to sets of intervals, Order, 39 (2022) 435-451.  arXiv:2011.07399.  DOI.  abstract.  MR4498500. 
• Which group algebras cannot be made zero by imposing a single non-monomial relation?  Communications in Algebra, 49 (2021) 3760-3776.  arXiv:1905.12704.  DOI.  abstract.  MR4290109. 
• On core quandles of groups, Communications in Algebra, 49 (2021) 2516-2537.  arXiv:2006.00641.  abstract & addenda.  MR3787805.  Example answering two questions asked in this note. 
• A note on factorizations of finite groups, Journal of the Iranian Mathematical Society, 1 (2020) 157-161.  arXiv:2003.12866.  abstract.  MR4532018. 
• Some results relevant to embeddability of rings (especially group algebras) in division rings, Journal of Algebra, 535 (2019) 503-540.  arXiv:1812.06123. abstract.  MR3982005. 
• Completeness results for metrized rings and lattices, Categories and General Algebraic Structures with Applications, special issue honoring George Grätzer, 11 (2019) 149-168.  arXiv:1808.04455.  abstract.  MR3988342. 
• Submonoids of groups, and group-representability of restricted relation algebras, Algebra Universalis (2018) 79:19 (15 pp).  DOI.  arXiv:1702.06088. abstract.  MR3787805. 
• Strong inner inverses in endomorphism rings of vector spaces, Publ. Mat. 62 (2018) 253-284.  DOI.  arXiv:1611.00972.  abstract.  MR3738191. 
• Simplicial complexes with lattice structures, Algebr. Geom. Topol. 17 (2017) 439-486.  DOI.  arXiv:1602.00034.  abstract.  MR3604382. 
• On Vaughan Pratt's crossword problem (with Pace P. Nielsen),  J. Lond. Math. Soc. (2) 93 (2016) 825-845.  DOI.  arXiv:1504.07310.   abstract.  MR3509966. 
• Adjoining a universal inner inverse to a ring element, J. Algebra, 449 (2016) 355-399.  DOI.  arXiv:1505.02312.  abstract.  MR3448178. 
• On [the] group topologies determined by families of sets, Matematychni Studii, 43 (2015) 115-128.  DOI.  arXiv:1311.2648.  abstract.  MR3444020. 
• Minimal faithful modules over artinian rings, Publicacions Matemàtiques, 59 (2015) 271-300.  DOI.  arXiv:1310.5365.  abstract.  MR3374608. 
• Homomorphisms on infinite direct products of groups, rings and monoids, Pacific Journal of Mathematics, 274 (2015) 451-495.  DOI.  arXiv:1406.1932.  abstract.  MR3332912. 
• Paul Moritz Cohn. 8 January 1924 -- 20 April 2006 (with Trevor Stuart), Biogr. Memoirs of Fellows of the Royal Society 60 (2014) 127-150.  DOI.  (I wrote sections 5-13, pp.137-148, on Cohn's research and publications.)  abstract. 
• Families of ultrafilters, and homomorphisms on infinite direct product algebras, J. Symb. Log. 79 (2014) 223–239. DOI.  arXiv:1301.6383.  abstract.  MR3226022
• On monoids, 2-firs and semifirs, Semigroup Forum 89 (2014) 293--335. DOI.  arXiv:1309.0564.  abstract.  MR3258484
• Thoughts on Eggert's Conjecture, pp.1-17 in Contemporary Mathematics, 609 (2014), Ring Theory and Its Applications, proceedings of a conference honoring T.Y.Lam.  DOI.  arXiv:1206.0326.  abstract.  MR3204348
• Homomorphic images of pro-nilpotent algebras,  Illinois J. Math., 55 (2011) 719–748.  (Actually appeared 2013.)  JSTOR.  DOI.  arXiv:0912.0020.  abstract and erratum.  MR3069281
• Continuity of homomorphisms on pro-nilpotent algebras,  Illinois J. Math., 55 (2011) 749–770.  (Actually appeared 2013.)  JSTOR.  DOI.  arxiv:1007.0223.  abstract.  MR3069282
• Every module is an inverse limit of injectives, Proc. A.M.S. 141 (2013) 1177-1183.  DOI.  arXiv:1104.3173.  abstract and addendum.  MR3008865
• Bilinear maps on Artinian modules, Journal of Algebra and its Applications, 11 (2012) No.5, 1250090, 10 pp.  DOI.  arXiv:1108.2520.  abstract.  MR2983182
• Isotone maps on lattices (with George Grätzer), Algebra Universalis, 68 (2012)  17-37.  DOI.  arXiv:1103.1339.  abstract.  MR3008736
• More abelian groups with free duals,  Portugaliae Mathematica, 69 (2012) 69-84.  DOI.  arXiv:1104.3827.  abstract.  MR2900652. 
• Linear maps on k^I, and homomorphic images of infinite direct product algebras (with Nazih Nahlus), J. Alg., 356 (2012) 257-274.  DOI.  arXiv:0910.5183.  abstract.  update.  MR2891132. 
• On diagram-chasing in double complexes, Theory and Applications of Categories 26 (2012) 60-96.  TeX source file of preprint (requires this style-class file).  arXiv:1108.0958.  abstract.  MR2909639. 
• An inner automorphism is only an inner automorphism, but an inner endomorphism can be something strange,  Publicacions Matemàtiques 56 (2012) 91-126.  DOI.  arXiv:1001.1391.  abstract.  update.  MR2918185
• Homomorphisms on infinite direct product algebras, especially Lie algebras (with Nazih Nahlus), J. Alg. 333 (2011) 67-104.  DOI.  arXiv:0910.5181.  abstract.  update.  MR2785938. 
• On common divisors of multinomial coefficients, Bull. Australian Math. Soc., 83 (2011) 138-157.  DOI.  arXiv:0806.0607.  abstract.  MR2765421. 
• On coproducts in varieties, quasivarieties and prevarieties, Algebra and Number Theory,  3 (2009) 847-879.  DOI.  arXiv:0806.1750.  abstract.  MR2587406. 
• Colimits of representable algebra-valued functors,  Theory and Applications of Categories, 20 (2008) 334-404.  TeX file of preprint (requires this style-class file).  arXiv:0711.0674.  abstract.  MR2425552. 
• On lattices and their ideal lattices, and posets and their ideal posets, Tbilisi Math. J.  1 (2008) 89-103.  (If you TeX the source file, you need this style-class file.)  abstract.  arXiv:0801.0751.  MR2563808. 
• Mapping radii of metric spaces, Pacific J. Math., 236 (2008) 223-261.  DOI.  arXiv:0704.0275.  abstract.  addenda and erratum.  MR2407106. 
• Some results on embeddings of algebras, after de Bruijn and McKenzie, Indagationes Mathematicae, 18 (2007) 349-403.  DOI.  arXiv:math.RA/0606407.  abstract.  update.  MR2373687. 
• Problem List, from Algebras, Lattices and Varieties, a conference in honor of Walter Taylor, held at the University of Colorado, 15-18 August, 2004, Algebra Universalis, 55 (2006) 509-526.  (I was just the record-keeper for this problem list.  My name appears under the title, with an error in my middle initial: "George W. Bergman (ed.)".) DOI.  MR2280306. 
• Two statements about infinite products that are not quite true, pp.35-58 in Groups, Rings and Algebras (Proceedings of a Conference in honor of Donald S. Passman), ed. W. Chin, J. Osterburg and D. Quinn, Contemporary Mathematics, v.420, 2006.  abstract.  DOI.  update.  MR:2279231. 
• Closed subgroups of the infinite symmetric group (with Saharon Shelah), Algebra Universalis, 55 (2006) 137-173.  abstract.  DOI.  arXiv:math.GR/0401305.  afterthoughts.  MR2280223. 
• Generating infinite symmetric groups, Bull. London Math. Soc., 38 (2006) 429-440.  DOI.  abstract.  arXiv:math.GR/0401304.  update.  MR2239037. 
• Can one factor the classical adjoint of a generic matrix? Transformation Groups, 11 (2006) 7-15.  DOI.  abstract.  MR2205070. 
• Direct limits and fixed-point sets, J. Algebra, 292 (2005) 592-614.  DOI.  arXiv:math.CT/0306127, MR2172170. 
• On lattices of convex sets in Rⁿ, Algebra Universalis, 53 (2005) 357-395.  DOI.  arXiv:math.MG/0409288, MR2148305. 
• Every finite semigroup is embeddable in a relatively free finite semigroup, J. Pure and Appl. Alg. 186 (2004) 1-19.  DOI.  MR2025909.
• Arrays of prime ideals in commutative rings, J. Algebra 261 (2003) 389-410.  DOI.  preprint (postscript) galleys (pdf) MR1966635 . 
• Constructing division rings as module-theoretic direct limits, Trans. Amer. Math. Soc., 354 (2002) no.5, 2079-2114.  DOI.  preprint (postscript).  MR1881031 .  Additional notes. 
• Infinite groups arising from partial presentations of finite groups, Math. Proc. Camb. Phil. Soc., 127 (1999) 425-439.  DOI.  preprint (postscript).  MR1713120 . 
• Supports of derivations, free factorizations, and ranks of fixed subgroups in free groups, Trans. Amer. Math. Soc., 351 (1999) 1531-1550.  DOI.  JSTOR.  preprint (dvi).  MR1458296 .  Update. 
• Linear ultrafilters, (with Ehud Hrushovski), Comm. Alg., 26 (1998) 4079-4113.  DOI.  preprint (postscript).  MR1661256 .  erratum and update. 
• On k-subspaces of L-vector-spaces, Comm. Alg., 26 (1998) 4115-4124.  DOI.  preprint (postscript).  MR1661288 . 
• On the growth of algebras with bialgebra action, Israel J. Math, 96 (1996), part A, pp.63-96.  preprint (dvi).  DOI.  MR1432727 .  (Erratum & additional ref.  at same J., 102 (1997) p.347.  DOI.  MR1489112 .) 
• Partially ordered sets, and minimal systems of counterexamples, Algebra Universalis 32 (1994) 13-30.  DOI.  MR1287014 . 
• Isomorphisms from top to bottom, pp.69-80 in Abelian groups and noncommutative rings.  A collection of papers in memory of Robert B. Warfield, Jr., ed. L. Fuchs., K. R. Goodearl, J. T. Stafford, C. Vinsonhaler.  Contemporary Mathematics 130 (1992).  DOI.  MR16061 . 
• Actions of Boolean rings on sets, Algebra Universalis 28 (1991) 153-187.  DOI.  MR1106053 . 
• Co-rectangular bands and cosheaves in categories of algebras, Algebra Universalis 28 (1991) 188-213 (assumes preceding).  DOI.  MR1106054 . 
• Right orderable groups that are not locally indicable, Pacific J. Math. 147 (1991) 243-248.  DOI.  MR1084707 .  addenda. 
• Infinite joins that are finitely join-irreducible (with Birge Zimmermann-Huisgen), Order 7 (1990) 27-40.  DOI.  MR1086125  (in MR paper rev., top line of 2nd col., delete "not"). 
• Ordering coproducts of groups and semigroups, J. Alg. 133 (1990) 313-339.  DOI.  MR1067409 .  unpublished addenda (postscript, 12 pp.)
• Radicals, tensor products, and algebraicity, pp.150-192 in Ring Theory 1989 in honor of S. A. Amitsur, ed. Louis Rowen, Weizmann Science Press of Israel, 1989.  MR1029309 .  unpublished addenda (postscript, 12 pp.)
• Subgroups close to normal subgroups (with Hendrik W. Lenstra, Jr.), J. Alg. 127 (1989) 80-97.  DOI.  MR1029404 . 
• HSP ≠ SHPS for metabelian groups, and related results, Algebra Universalis 26 (1989) 267-283.  DOI.  MR1044848 .  erratum and updates. 
• Gel'fand-Kirillov dimensions of factor rings, Comm. Alg. 16 (1988) 2555-2567.  DOI.  MR0955325 . 
• Embedding arbitrary algebras in groups, Algebra Universalis 25 (1988) 107-120.  DOI.  MR0950739 .  
• On the scarcity of contravariant left adjunctions, Algebra Universalis 24 (1987) 169-185.  DOI.  MR0921541 . 
• The amalgamation basis of the category of compact groups, manuscripta mathematica 58 (1987) 253-281.  DOI.  MR0921541. 
• Transversals of families in complete lattices and torsion in product modules (with Fred Galvin), Order 3 (1987) 391-403.  DOI.  MR0891386. 
• Normalizers of semifirs in their universal fields, Proc. London Math. Soc. (3) 54 (1987) 83-87.  DOI.  MR0872251 . 
• Weakening partial orderings to lattice and semilattice orderings, Order 3 (1986) 283-286.  DOI.  MR0878924 . 
• Identities of cofinal sublattices (with Ehud Hrushovski), Order 2 (1985) 173-191.  DOI.  MR0815863 . 
• Everybody knows what a Hopf algebra is, pp. 25-48 in Group Actions on Rings (proceedings of a conference on group actions, Bowdoin College, Bowdoin, Maine, July 18-24, 1984) ed. S. Montgomery, Contemp. Math. 43 (1985).  DOI.  MR0810641 . 
• A cofinal coloring theorem for partially ordered algebras (with Irving Kaplansky), Order 1 (1985) 259-263.  DOI.  MR0779391 . 
• Specially ordered groups, Communications in Algebra 12 (1984) 2315-2333.  DOI.  MR0755918 . 
• Some examples of non-compressible rings, Communications in Algebra 12 (1984) 1-8.  DOI.  MR0732181 . 
• Sfields finitely right-generated over subrings, Communications in Algebra 11 (1983) 1893-1902.  DOI.  MR0709020 . 
• Embedding rings in completed graded rings.  1. Triangular embeddings, J. Alg. 84 (1983) pp.14-24.  DOI.  MR0716768 . 
• Embedding rings in completed graded rings.  2. Algebras over a field (with Samuel M. Vovsi), J. Alg. 84 (1983) pp.25-41.  DOI.  MR0716769 . 
• Embedding rings in completed graded rings.  3. Algebras over general k (with D. J. Britten and F. W. Lemire), J. Alg. 84 (1983) pp.42-61 (assumes part 2).  DOI.  MR0716770 . 
• Embedding rings in completed graded rings.  4. Commutative algebras, J. Alg. 84 (1983) pp.62-106 (some sections assume parts 2 and 3, but development of main result is self-contained).  DOI.  MR0716771 . 
• Hyperidentities in groups and semigroups, Aequationes Mathematicae 23 (1981) 50-65.  DOI.  MR0667217 .  updates.  (Previewed at Aequationes Mathematicae 22 (1981) 315-317  MR0645428 . )
• The rank of a two-dimensional cylindric set algebra, pp.95-105 in Universal Algebra, Esztergom (Hungary) 1977, Colloq. Math. Soc. Janos Bolyai, v.29, 1982.  MR0660851 . 
• Gel'fand-Kirillov dimension can go up in extension modules, Communications in Algebra 9 (1981) 1567-1570.  DOI.  MR0630326 . 
• Universal derivations and universal ring constructions (with Warren Dicks), Pacific J. Math. 79 (1978) 293-337.  DOI.  MR0531320 .  Here are some addenda by my coauthor. 
• The diamond lemma for ring theory, Advances in Mathematics 29 (1978) 178-218.  DOI.  MR0506890 .  errata and updates.  Wikipedia 
• Conjugates and nth roots in Hahn-Laurent group rings, Bull. Malaysian Math. Soc. (2) 1 (1978) 29-41; historical addendum at (2) 2 (1979) 41-42.  MR0506536 , MR0545801 . 
• Terms and cyclic permutations, Algebra Universalis 8 (1978) 129-130.  DOI.  MR0457243 . 
• On the existence of subalgebras of direct products with prescribed d-fold projections, Algebra Universalis 7 (1977) 341-356.  DOI.  MR0453608 . 
• Zero-divisors in tensor products, pp. 32-82 of SLNM v.545, Noncommutative ring theory, papers presented at the international conference at Kent State University, 4-5 April 1975, Springer Verlag, 1976.  DOI.  MR0439871 .  update. 
• Rational relations and rational identities in division algebras, I, J. Alg. 43 (1976), 252-266.  DOI.  MR0432697 . 
• Rational relations and rational identities in division algebras, II, J. Alg. 43 (1976) 267-297 (assumes part I).  DOI.  MR0432698 . 
• Some category-theoretic ideas in algebra, pp. 285-296 of Proceedings of the 1974 International Congress of Mathematicians (Vancouver) v. I, Canadian Mathematical Congress, 1975.  PDF.  MR0506544 . 
• On universal derivations (with Warren Dicks), J. Alg. 36 (1975) 193-211.  DOI.  MR0387353 . 
• The semigroup of ideals of a fir is (usually) free (with Jacques Lewin), J. London Math. Soc. (2) 11 (1975) 21-31.  DOI.  MR0379554 . 
• P.i. degrees and prime ideals (with Lance W. Small), J. Alg. 33 (1975) 435-462.  DOI.  MR0360682 . 
• Some examples in PI ring theory, Israel J. Math. 18 (1974) 257-277.  DOI.  MR0357488 .  Errata and updates. 
• Modules over coproducts of rings, Trans. A.M.S. 200 (1974) 1-32.  DOI.  JSTOR.  MR0357502 . 
• Coproducts and some universal ring constructions, Trans. A.M.S. 200 (1974) 33-88 (assumes preceding).  DOI.  JSTOR.  MR0357503 .  erratum and updates. 
• The Zariski topology and generalizations, pp.32-39 in Topology and its Applications, (proceedings of a symposium in Budva, Jugoslavia, Aug. 1972), Beograd 1973.  MR0345964 . 
• Rings with fixed-point-free group actions (with I. M. Isaacs), Proc. London Math. Soc. (3) 27 (1973) 69-87.  DOI.  MR0346017 . 
• The automorphism class group of the category of rings (with W. Edwin Clark), J. Alg. 24 (1973) 80-99.  DOI.  MR0311648 . 
• Infinite multiplication of ideals in ℵ₀-hereditary rings, J. Algebra 24 (1973) 56-70.  DOI.  MR0309982 .  errata. 
• Boolean rings of projection maps, J. London Math. Soc. (2) 4 (1972) 593-598.  DOI.  MR0311531 . 
• Hereditarily and cohereditarily projective modules, pp.29-62 in Ring Theory (proceedings of a conference held in Park City, UT March 2-6 1971), Robert Gordon ed., Academic Press 1972. 394 pp..  MR0393124 . 
• Nakayama's Lemma for half-exact functors (with Arthur Ogus), Proc. A.M.S. 31 (1972) 67-74.  DOI.  JSTOR.  MR0302633 . 
• Sulle classi filtrali di algebre (Italian), Annali dell'Univ. di Ferrara (NS) Sez. VII 17 (1971) 35-42.    MR0304267 . 
• Hereditary commutative rings, and centres of hereditary rings, Proc. London Math. Soc (3) 23 (1971) 214-236.  DOI.  MR0309918 . 
• Centres of 2-firs and hereditary rings (with P. M. Cohn), Proc. London Math. Soc (3) 23 (1971) 83-98.  DOI.  MR0291200 . 
• Groups acting on hereditary rings, Proc. London Math. Soc (3) 23 (1971) 70-82.  DOI.  (corrigendum to Theorem 4.2 at (3) 24 (1972) 192, DOI.)  MR0291199 . 
• The logarithmic limit-set of an algebraic variety, Trans. A.M.S. 157 (1971) 459-469.  DOI.  JSTOR.  MR0280489 .  errata and update. 
• A weak Nullstellensatz for valuations, Proc. A.M.S. 28 (1971) 32-38.  DOI.  JSTOR.  MR02727801 . 
• The index of a group in a semigroup, Pacific J. Math. 36 (1971) 55-62.  DOI.  MR0274619 . 
• Skew fields of rational functions, after Amitsur (by `George W. Bergman'), Séminaire M. P. Schützenberger, A. Lentin et M. Nivat, Année 1969/70, Problèmes Mathématiques de la théorie des automates, Secrétariat mathématique, 11 Rue Pierre et Marie Curie, 75 - Paris 5.  MR0280540 . 
• Symmetric elements in free powers of rings (with P. M. Cohn), J. London Math. Soc. (2) 1 (1969) 525-534.  DOI.  MR0251070 . 
• Ranks of tensors and change of base field, J. Alg. 11 (1969) 613-621.  DOI.  MR0242850 . 
• Centralizers in free associative algebras, Trans. A.M.S. 137 (1969) 327-344.  DOI.  JSTOR.  MR0236208 . 
• On groups acting on locally finite graphs, Annals of Math. 88 (1968) 335-340.  DOI.  JSTOR.  MR0228574 . 
• A fixed-point theorem for inward and outward maps (with Benjamin R. Halpern), Trans. A.M.S. 130 (1968) 353-358.  DOI.  JSTOR.  MR0221345 . 
• Connected fields of arbitrary characteristic (with Alan G. Waterman), J. Math. Kyoto U. 5 (1966) 174-184.  MR0201430
• Section on ring schemes and Witt vectors (pp. 171-191) in: David Mumford, Lectures on curves on an algebraic surface, with a section by G. M. Bergman, Annals of Math. Studies, No.59, Princeton University Press, Princeton, 1966.  MR0209285 . 
• A counterexample in differential algebra, Proc. A.M.S. 16 (1965) 1407-1409.  DOI.  JSTOR.  MR0186670 . 
• A ring primitive on the right but not on the left, Proc. A.M.S. 15 (1964) 473-475.  DOI.  JSTOR.  MR0167497 , Errata at ibid. p.1000.  JSTOR:errata.  MR0175940 . 
• A number system with an irrational base, Mathematics Magazine 31 (1957/58) 98-110.  DOI.  JSTOR.  MR0131384 .