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Field name	Details
Dewey Class	511.33
Title	Lattice Concepts of Module Theory ([EBook] /) / by Grigore Călugăreanu.
Author	Călugăreanu, Grigore
Other name(s)	SpringerLink (Online service)
Publication	Dordrecht : : Springer Netherlands : : Imprint: Springer, , 2000.
Physical Details	XIII, 225 p. : online resource.
Series	Springer Texts in the Mathematical Sciences, A Graduate-Level Book Series 0927-4529 ; ; 22
ISBN	9789401595889
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-94-015-9588-9
Links to Related Works	Subject References: Algebra . Associative rings . Associative Rings and Algebras . Commutative algebra . Commutative rings . Commutative Rings and Algebras . Group theory . Group Theory and Generalizations . Mathematics . Order, Lattices, Ordered Algebraic Structures . Ordered algebraic structures . Rings (Algebra) . Authors: Călugăreanu, Grigore . Corporate Authors: SpringerLink (Online service) . Series: Springer Texts in the Mathematical Sciences, A Graduate-Level Book Series . Classification: 511.33 .

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Lattice Concepts of Module Theory

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