Lattice Concepts of Module Theory - Grigore Calugareanu

Lattice Concepts of Module Theory

Buch | Hardcover
225 Seiten
2000
Springer (Verlag)
978-0-7923-6488-7 (ISBN)
106,99 inkl. MwSt
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.
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.

1 Basic notions and results.- 2 Compactly generated lattices.- 3 Composition series. Decompositions.- 4 Essential elements. Pseudo—complements.- 5 Socle. Torsion lattices.- 6 Independence. Semiatomic lattices.- 7 Radical. Superfluous and fully invariant elements.- 8 Lattices of finite uniform dimension.- 9 Purity and neatness in lattices.- 10 Coatomic lattices.- 11 Co—compact lattices.- 12 Supplemented lattices. Locally artinian lattices.- 13 Several dimensions.- 14 Solutions of exercises.

Erscheint lt. Verlag 31.8.2000
Reihe/Serie Texts in the Mathematical Sciences ; 22
Zusatzinfo XIII, 225 p.
Verlagsort Dordrecht
Sprache englisch
Maße 156 x 234 mm
Themenwelt Mathematik / Informatik Mathematik Algebra
ISBN-10 0-7923-6488-0 / 0792364880
ISBN-13 978-0-7923-6488-7 / 9780792364887
Zustand Neuware
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