ERRATA, UPDATES, AND OTHER NOTES REGARDING
George M. Bergman and Adam O. Hausknecht,
Cogroups and co-rings in categories of associative
rings,
American Mathematical Society, Mathematical Surveys and
Monographs #45, 1996.
IMPORTANT ERRATA: None yet -- have patience! (or send me some)
MINOR ERRATA:
Pp. 29, 67, 223, 325: the section whose title is shown at the
top of each of these pages actually begins on the next page.
P.177, three lines above Theorem 33.7: the reference
to "Theorem 23.9(i)" should be to Theorem 25.1(i).
P.188, paragraph following Theorem 34.24: between the second and
third sentences, the stranded words "a field." should be deleted.
P.283, last full line: "overgroup of B'"
should be "overgroup B'".
P.366, the page number reference for "dependence among chapters and
sections" should be ix, not iii.
OTHER NOTES:
Pp.240-256 (§§45-47): It would be interesting to
examine the relationship between the ring of representative
integer-valued functions on a free group G (§47), and
the ring of word functions on G as defined in
[205] (see below).
The latter could also be looked at as a generalization of the ring of
integral polynomials, discussed in §§45-46. Indeed, the
word functions on the group Z are precisely the integral
polynomials.
UPDATES to bibliography:
24.
A published edition of those lecture notes has appeared:
George M. Bergman,
An Invitation to General Algebra and Universal Constructions,
2015, Springer Universitext, 572 pp.
DOI 10.1007/978-3-319-11478-1,
ISBN9 78-3-319-11477-4,
eBook ISBN 978-3-319-11478-1.
(First edition: ISBN 0-9655211-4-1, published by Henry Helson, 1998
MR 99h:18001 .)
In those editions, there are changes in the numbering
of results we refer to.
Most noticeable, in the 2015 version, all chapter numbers
have increased by 1
(because Springer's macro packages didn't allow a "Chapter 0").
Here are some other changes,
listed by the relevant page numbers in Bergman-Hausknecht.
I give the new numbering as in the 2015 edition of the
book; for the 1998 version, decrease the chapter-numbers by 1.
P.29. The results of [24] referred to on the last three
lines as "Theorem 7.9.4" and "Exercises 7.9:5-7.9:6
and 9.4:4" have
become "Theorem 8.10.4", and "Exercises 8.10:4-8.10:5 and 10.5:5".
P.89, first paragraph of Sketch of Proof.
The results of [24] referred to as "Corollary 7.7.2"
and "Proposition 7.7.3" are now "Theorem 8.8.3" and
"Theorem 8.8.6".
26. This has appeared:
George M. Bergman, Colimits of representable algebra-valued
functors,
Theory and Applications of Categories, 20 (2008) 334-404.
[dvi]
[ps]
[pdf]
MR 2009c:18012
70.
The "Erratum to appear"
has appeared: same journal, 80 (1995) p.293, and
the paper has been reviewed in Math Reviews: MR96a:18004.
173.
This has also been reviewed: MR95m:16033.
Here are two new references, referred to under OTHER NOTES above:
205. Jean Eric Pin and Christophe Reutenauer,
A conjecture on the Hall topology for the free group,
Bull. Lond. Math. Soc. 23 (1991) 356-362.
(Note: the conjecture discussed in this paper
is proved in [206].)
MR92g:20035.
206. Luis Ribes and Pavel A. Zalesskii,
On the profinite topology on a free group,
Bull. London Math. Soc., 25 (1993) 37-43.
MR93j:20062.
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