##### 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*: MR**96a**:18004.

**173.**
This has also been reviewed: MR**95m**: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**].)
MR**92g**:20035.

**206.** Luis Ribes and Pavel A. Zalesskii,
*On the profinite topology on a free group*,
Bull. London Math. Soc., **25** (1993) 37-43.
MR**93j**:20062.

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