Semidistributive Modules and Rings (Paperback, Softcover reprint of the original 1st ed. 1998)

A module M is called distributive if the lattice Lat(M) of all its submodules is distributive, i.e., Fn(G + H) = FnG + FnH for all submodules F, G, and H of the module M. A module M is called uniserial if all its submodules are comparable with respect to inclusion, i.e., the lattice Lat(M) is a chain. Any direct sum of distributive (resp. uniserial) modules is called a semidistributive (resp. serial) module. The class of distributive (resp. semidistributive) modules properly cont.ains the class ofall uniserial (resp. serial) modules. In particular, all simple (resp. semisimple) modules are distributive (resp. semidistributive). All strongly regular rings (for example, all factor rings of direct products of division rings and all commutative regular rings) are distributive; all valuation rings in division rings and all commutative Dedekind rings (e.g., rings of integral algebraic numbers or commutative principal ideal rings) are distributive. A module is called a Bezout module or a locally cyclic module ifevery finitely generated submodule is cyclic. If all maximal right ideals of a ring A are ideals (e.g., if A is commutative), then all Bezout A-modules are distributive

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Mathematics and Its Applications, 449
Release date:	October 2012
First published:	1998
Authors:	A. a. Tuganbaev
Dimensions:	240 x 160 x 20mm (L x W x T)
Format:	Paperback
Pages:	357
Edition:	Softcover reprint of the original 1st ed. 1998
ISBN-13:	978-9401061360
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General
LSN:	940106136X
Barcode:	9789401061360

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