232 Pages
by
Chapman & Hall
232 Pages
by
Chapman & Hall
Also available as eBook on:
Because traditional ring theory places restrictive hypotheses on all submodules of a module, its results apply only to small classes of already well understood examples. Often, modules with infinite Goldie dimension have finite-type dimension, making them amenable to use with type dimension, but not Goldie dimension. By working with natural classes and type submodules (TS), Classes of Modules... Read more
PRELIMINARY BACKGROUND
Notation and Terminology
Lattices
IMPORTANT MODULE CLASSES AND CONSTRUCTIONS
Torsion Theory
The Module Class s[M]
Natural Classes
M-Natural Classes
Pre-Natural Classes
FINITENESS CONDITIONS
Ascending Chain Conditions
Descending Chain Conditions
Covers and Ascending Chain Conditions
TYPE THEORY OF MODULES: DIMENSION
Type Submodules and Type Dimensions
Several Type Dimension Formulas
Some Non-Classical Finiteness Conditions
TYPE THEORY OF MODULES: DECOMPOSITIONS
Type Direct Sum Decompositions
Decomposability of Modules
Unique Type Closure Modules
TS-Modules
LATTICES OF MODULE CLASSES
The Lattice of Pre-Natural Classes
More Sublattice Structures
Lattice Properties of Npr (R)
More Lattice Properties of Npr (R)
The Lattice Nr(R) and Its Applications
The Boolean Ideal Lattice
REFERENCES
INDEX
Notation and Terminology
Lattices
IMPORTANT MODULE CLASSES AND CONSTRUCTIONS
Torsion Theory
The Module Class s[M]
Natural Classes
M-Natural Classes
Pre-Natural Classes
FINITENESS CONDITIONS
Ascending Chain Conditions
Descending Chain Conditions
Covers and Ascending Chain Conditions
TYPE THEORY OF MODULES: DIMENSION
Type Submodules and Type Dimensions
Several Type Dimension Formulas
Some Non-Classical Finiteness Conditions
TYPE THEORY OF MODULES: DECOMPOSITIONS
Type Direct Sum Decompositions
Decomposability of Modules
Unique Type Closure Modules
TS-Modules
LATTICES OF MODULE CLASSES
The Lattice of Pre-Natural Classes
More Sublattice Structures
Lattice Properties of Npr (R)
More Lattice Properties of Npr (R)
The Lattice Nr(R) and Its Applications
The Boolean Ideal Lattice
REFERENCES
INDEX
Biography
John Dauns, Yiqiang Zhou
"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
