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Basic algebra II. 2nd ed. (English) Zbl 0694.16001

New York, NY: W. H. Freeman and Company. xvii, 686 p. £37.95 (1989).
This is the second edition of Volume 2 of the author’s work entitled “Basic algebra”. The main differences between this and the first edition (1980; Zbl 0441.16001) are in the section devoted to commutative algebra. In the chapter on commutative ideal theory there is an improved account of integral dependence, and a new section is added on integrally closed domains. In the chapter on field theory three new sections are added: transcendency bases for domains; tensor products of fields; and free composites of fields (the latter two being taken from volume 3 of the author’s “Lectures in abstract algebra” (1980; Zbl 0455.12001). In the chapter on homological algebra an improved proof is given of the existence of a projective resolution of a short exact sequence of modules. Some new exercises are added, and defective ones removed.
Reviewer: T.S.Blyth

MSC:

16-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to associative rings and algebras
13-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra
12-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to field theory
18-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to category theory
16-02 Research exposition (monographs, survey articles) pertaining to associative rings and algebras
12-02 Research exposition (monographs, survey articles) pertaining to field theory
13-02 Research exposition (monographs, survey articles) pertaining to commutative algebra
18-02 Research exposition (monographs, survey articles) pertaining to category theory
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