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.
In that version, there are changes in the numbering
of results we refer to.
Most noticeably, 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.
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.