Harry Hutchins "Examples of commutative rings" may be of interest.
It is based on his 1978 Chicago Ph.D. thesis under
Kaplansky, and not surprisingly it serves as a useful complement to
Kaplansky's excellent textbook Commutative Rings (most references
to proofs refer to Kaplansky). There is also a 3 page list of
errata, updates,... dated July 1983, which is distributed with the book.
Hutchins, Harry C. 83a:13001 13-02
Examples of commutative rings. (English)
Polygonal Publ. House, Washington, N. J., 1981. vii+167 pp. $13.75. ISBN 0-936428-05-8
The book is divided into two parts: a brief sketch of commutative ring theory
which includes pertinent definitions along with main results without proof
(but with ample references), and Part II, the 180 examples. The examples do
cover a very large range of topics. Although most of them appear elsewhere,
they are enhanced by a fairly complete listing of their properties. Example
67, for instance, is M. Hochster's counterexample to the polynomial
cancellation problem, and it lists a number of properties of the two rings
that were not given in the original paper Proc. Amer. Math. Soc. 34 (1972),
no. 1, 81 - 82; MR 45 #3394. Some of the examples appear more than once,
since many rings exhibit more than one interesting property. (R=Kx, y, z is
used in Examples 6 and 22.) The examples are grouped into areas, but a
drawback is that these have not been labeled and separated off. In addition,
the Index is for Part I and definitions only, and this means that searching
for a specific example with certain properties can be time consuming. The book
can be used as a supplement to one of the standard texts in commutative ring
theory, and it does appear to complement the monograph by I. Kaplansky
Commutative rings, Allyn and Bacon, Boston, Mass., 1970; MR 40 #7234;
second edition, Univ. Chicago Press, Chicago, Ill., 1974; MR 49 #10674.
--Reviewed by Jon L. Johnson
No comments:
Post a Comment