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.