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)

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. 

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. 

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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