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Zusatztext "This nice book is written in a very clear and explanatory style! offering a self-contained presentation as well as illustrative examples! and demonstrating how the themes of (pre-) natural classes and type submodules structure much of Ring and Module Theory. I believe that I should be on the desk of anybody working in this area of Algebra." - Toma Albu! in Mathematical Reviews! 2007m Informationen zum Autor John Dauns, Yiqiang Zhou Klappentext Classes of Modules demonstrates that in the next generation of ring and module theory! it will be very important to work with the type dimension of a module! natural classes! and type submodules. This book presents the concepts of type dimension! a natural class! and a type submodule! by exploring how they enter into much of ring and module theory. It carefully develops the foundations of the subject and the advanced theorems. Self-contained! accessible! and well-suited for those with some background in basic ring and module theory! this text compiles material that was previously scattered throughout the literature! along with improved and extended results as well as simplified proofs. Zusammenfassung Presents the concepts of type dimension, a natural class, and a type submodule, by exploring how they enter into much of ring and module theory. This book develops the foundations of the subject and the advanced theorems. It is suitable for those with some background in basic ring and module theory. Inhaltsverzeichnis PRELIMINARY BACKGROUNDNotation and TerminologyLatticesIMPORTANT MODULE CLASSES AND CONSTRUCTIONSTorsion TheoryThe Module Class s[M]Natural ClassesM-Natural ClassesPre-Natural ClassesFINITENESS CONDITIONSAscending Chain ConditionsDescending Chain ConditionsCovers and Ascending Chain ConditionsTYPE THEORY OF MODULES: DIMENSIONType Submodules and Type DimensionsSeveral Type Dimension FormulasSome Non-Classical Finiteness ConditionsTYPE THEORY OF MODULES: DECOMPOSITIONSType Direct Sum DecompositionsDecomposability of ModulesUnique Type Closure ModulesTS-ModulesLATTICES OF MODULE CLASSESThe Lattice of Pre-Natural ClassesMore Sublattice StructuresLattice Properties of Npr (R) More Lattice Properties of Npr (R) The Lattice Nr(R) and Its Applications The Boolean Ideal LatticeREFERENCESINDEX ...
