Lattice Concepts of Module Theory (Hardcover, 2000 ed.)

Grigore Calugareanu

Series: Texts in the Mathematical Sciences, 22

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It became more and more usual, from, say, the 1970s, for each book on Module Theory, to point out and prove some (but in no more than 15 to 20 pages) generalizations to (mostly modular) lattices. This was justified by the nowadays widely accepted perception that the structure of a module over a ring is best understood in terms of the lattice struc ture of its submodule lattice. Citing Louis H. Rowen "this important example (the lattice of all the submodules of a module) is the raison d'etre for the study of lattice theory by ring theorists". Indeed, many module-theoretic results can be proved by using lattice theory alone. The purpose of this book is to collect and present all and only the results of this kind, although for this purpose one must develop some significant lattice theory. The results in this book are of the following categories: the folklore of Lattice Theory (to be found in each Lattice Theory book), module theoretic results generalized in (modular, and possibly compactly gen erated) lattices (to be found in some 6 to 7 books published in the last 20 years), very special module-theoretic results generalized in lattices (e. g. , purity in Chapter 9 and several dimensions in Chapter 13, to be found mostly in [27], respectively, [34] and [18]) and some new con cepts (e. g.

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Texts in the Mathematical Sciences, 22
Release date:	2001
First published:	2000
Authors:	Grigore Calugareanu
Dimensions:	234 x 156 x 15mm (L x W x T)
Format:	Hardcover
Pages:	225
Edition:	2000 ed.
ISBN-13:	978-0-7923-6488-7
Categories:	Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory Promotions
LSN:	0-7923-6488-0
Barcode:	9780792364887