Modules over discrete valuation domains.

9783110200539

Modules over discrete valuation domains.

Krylov, Piotr A. and Askar A. Tuganbaev.

Walter de Gruyter

2008

357 pages

$168.00

Hardcover

De Gruyter expositions in mathematics; 43

QA177

These modules play important roles in various areas of algebra, primarily commutative algebra, including rings of p-adic integers and certain power series rings over division rings. Krylov and Tuganbaev consider all main areas of the theory of modules over discrete valuation domains, including those related to Abelian groups. They include a range of exercises in their coverage of basic facts on modules, endomorphism rings of divisible and complete modules, representation of rings by endomorphism rings, torsion-free modules, mixed modules, determination of modules by their endomorphism rings, and modules with many endomorphisms or automorphisms. Readers should be familiar with basic concepts of the theory of rings and modules, and the authors recommend references for these topics.

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