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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