Classes of Modules
Regular price
€173.60
A01=John Dauns
A01=Yiqiang Zhou
advanced ring theory
algebraic chain conditions
Author_John Dauns
Author_Yiqiang Zhou
boolean
Boolean ideal analysis
Boolean Lattice
Boolean Ring
Category=PBF
Category=PBH
complement
Complement Submodule
Complete Sublattice
Direct Sum
Direct Summands
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Essential Submodule
Finite Uniform Dimension
Goldie Torsion
Hereditary Torsion
Hereditary Torsion Theory
hull
injective
Injective Hull
lattice
Local Summand
module decomposition methods
natural class decomposition in algebra
Nonsingular Modules
Nonsingular Ring
Nonzero Submodule
ordered
partially
Pre-natural Class
Prenatural Classes
Quasi-injective Module
quotient
Quotient Ring
Regular Open Sets
right module lattices
ring
set
Square Free Module
Torsion Free Class
Torsion Theory
TS-module structures
Unique Simple Module
Product details
- ISBN 9781584886600
- Weight: 467g
- Dimensions: 145 x 226mm
- Publication Date: 19 Jun 2006
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
Secure
checkout
Fast Shipping
Easy returns
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 develops the foundations and tools for the next generation of ring and module theory. It shows how to achieve positive results by placing restrictive hypotheses on a small subset of the complement submodules, Furthermore, it explains the existence of various direct sum decompositions merely as special cases of type direct sum decompositions.
Carefully developing the foundations of the subject, the authors begin by providing background on the terminology and introducing the different module classes. The modules classes consist of torsion, torsion-free, s[M], natural, and prenatural. They expand the discussion by exploring advanced theorems and new classes, such as new chain conditions, TS-module theory, and the lattice of prenatural classes of right R-modules, which contains many of the previously used lattices of module classes. The book finishes with a study of the Boolean ideal lattice of a ring.
Through the novel concepts presented, Classes of Modules provides a new, unexplored direction to take in ring and module theory.
