George M. Bergman

Professor Emeritus, Professor of the Graduate School
Primary Research Area: 
Additional Research Areas: 
Mathematical Logic
Research Interests: 
Associative rings, Universal algebra and category theory, Counterexamples
Contact Information
865 Evans Hall
gbergman [at] math [dot] berkeley [dot] edu
Year Appointed: 
Selected Publications: 
  1. George M. Bergman (2023), An elementary result on infinite and finite direct sums of modules, Journal of Algebra, 631 (2023) 731-737.  [pdf] [MR] [arXiv]
  2. George M. Bergman (2019), Some results relevant to embeddability of rings (especially group algebras) in division rings, Journal of Algebra, 535 (2019) 503-540.  [DOI] [pdf]  [MR] [tex] [arXiv]
  3. George M. Bergman (2015), An invitation to general algebra and universal constructions, 2nd edn., Springer Universitext, x+572 pp. ISBN 978-3-319-11477-4 [DOI] [pdf] [MR], [MR, 1st edn] [ZM]
  4. George M. Bergman (2011). Homomorphic images of pro-nilpotent algebras. Illinois J. Math., 55 (2011) 719-748. [tex] [dvi] [ps] [pdf] [abstract] [arXiv] [MR] [projecteuclid]
  5. George M. Bergman (2006). Generating infinite symmetric groups. Bull. London Math. Soc. 38 429-440. [tex] [dvi] [ps] [doi] [update] [arXiv] [MR]
  6. George M. Bergman and Adam O. Hausknecht (1996). Co-groups and co-rings in categories of associative rings. Mathematical Surveys and Monographs, Vol. 45. American Mathematical Society Providence, RI x+388. [updates & errata] [MR] [ZM][ams_bookstore]
  7. George M. Bergman (1983). Embedding rings in completed graded rings. IV. Commutative algebras. J. Algebra 84 No.1, 62-106. [doi] [MR] [ZM]
  8. George M. Bergman (1978). The diamond lemma for ring theory. Adv. in Math. 29 No.2, 178-218. [doi] [errata & updates] [MR] [ZM]
  9. George Bergman (1976). Rational relations and rational identities in division rings. II. J. Algebra 43 No.1, 267-297. [doi] [MR] [ZM]
  10. George M. Bergman (1974). Coproducts and some universal ring constructions. Trans. Amer. Math. Soc. 200 33-88. [JSTOR] [erratum & updates] [MR] [ZM]