Multiplicative ideal theory.
Rev. ed.

*(English)*Zbl 0804.13001
Queen’s Papers in Pure and Applied Mathematics. 90. Kingston: Queen’s University, x, 609 p. (1992).

This is a revised edition of the text first published in 1972 (see Zbl 0248.13001). The main additions to the text consist of

(i) a new first section to chapter III (Valuation theory) on partially ordered abelian groups with consequential changes to the following two sections,

(ii) a section on Hilbert rings in chapter V (Polynomial rings),

(iii) sections on algebraic number fields and prime factorization of principal ideals in chapter VI (Classical ideal theory).

In addition each chapter now ends with “Allerlei” which are general remarks on the material of the chapter and references for sources and for further reading. This new version also includes around 1000 exercises of variable depth, the harder problems have references to original papers. Finally the bibliography has been reduced by about one half by retaining only sources referred to in the text.

(i) a new first section to chapter III (Valuation theory) on partially ordered abelian groups with consequential changes to the following two sections,

(ii) a section on Hilbert rings in chapter V (Polynomial rings),

(iii) sections on algebraic number fields and prime factorization of principal ideals in chapter VI (Classical ideal theory).

In addition each chapter now ends with “Allerlei” which are general remarks on the material of the chapter and references for sources and for further reading. This new version also includes around 1000 exercises of variable depth, the harder problems have references to original papers. Finally the bibliography has been reduced by about one half by retaining only sources referred to in the text.

Reviewer: D.Kirby (Southampton)

##### MSC:

13A15 | Ideals and multiplicative ideal theory in commutative rings |

13-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra |