Lattice Concepts of Module Theory - Couverture souple

Calugareanu, Grigore

Couverture souple

ISBN 10 : 9048155304 ISBN 13 : 9789048155309

Editeur : Springer, 2010

Synopsis

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.

A propos du livre

Présentation de l'éditeur

This volume is dedicated to the use of lattice theory in module theory. Its main purpose is to present all module-theoretic results that can be proved by lattice theory only, and to develop the theory necessary to do so. The results treated fall into categories such as the origins of lattice theory, module-theoretic results generalised in modular and likely compactly generated lattices, very special module-theoretic results generalised in lattices, and new concepts in lattices introduced by the author.
Audience: This book will be of interest to graduate students and researchers whose work involves order, lattices, group theory and generalisations, general module theory, and rings and algebras.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2010
• Langue: anglais
• ISBN 10: 9048155304
• ISBN 13: 9789048155309
• Reliure: Broché
• Numéro d'édition: 1
• Nombre de pages: 240
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Allemagne