Lattice Concepts of Module Theory by Grigore CalugareanuLattice Concepts of Module Theory by Grigore Calugareanu

Lattice Concepts of Module Theory

byGrigore Calugareanu

Paperback | December 8, 2010

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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.
Title:Lattice Concepts of Module TheoryFormat:PaperbackDimensions:225 pages, 24.4 × 17 × 0.01 inPublished:December 8, 2010Publisher:Springer-Verlag/Sci-Tech/TradeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048155304

ISBN - 13:9789048155309


Table of Contents

Preface. List of Symbols. 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. Bibliography. Index.