Commutator Theory for Congruence Modular Varieties by Ralph Freese, Ralph McKenzie
About this book :-
This text is about understanding how certain types of mathematical structures work. It looks at something called commutators and how they behave in certain kinds of algebraic structures, called varieties. It cover the basic theory of commutators in congruence modular varieties and some of its strongest applications. The authors take an algebraic approach, using some of the shortcuts that Taylor and others have discovered.
A commutator can be defined rather naturally in the congruence lattices of every congruence modular variety. This operation has the same useful properties that the commutator for groups (which is a special case of it) possesses. The resulting theory has many general applications and, we feel, it is quite beautiful. In this book we present the basic theory of commutators in congruence modular varieties and some of its strongest applications. This book developed a sustained analogy between commutator theory and affine geometry which allowed him to discover many of the basic facts about the commutator.
Book Detail :-
Title:
Commutator Theory for Congruence Modular Varieties by Ralph Freese, Ralph McKenzie
Publisher:
Cambridge University Press
Year:
1984
Pages:
174
Type:
PDF
Language:
English
ISBN-10 #:
0521348323
ISBN-13 #:
9780521348324
License:
Linked Content Owned by Author
Amazon:
Amazon
About Author :-
The author
Ralph Freese
Ralph Freese is a Emeritus Professor of Mathematics at Department of Mathematics, University of Hawaii. He is Ph.D. of Calif. Inst. of Tech. His research interests is Lattice Theory and General Algebra.
Book Contents :-
1. The Commutator in Groups and Rings
2. Universal Algebra
3. Several Commutators
4. One Commutator in Modular Varieties;Its Basic Properties
5. The Fundamental Theorem on Abelian Algebras
6. Permutability and a Characterization ofModular Varieties
7. The Center and Nilpotent Algebras
8. Congruence Identities 59
9. Rings Associated With Modular Varieties: Abelian Varieties
10. Structure and Representationin Modular Varieties
11. Joins and Products of Modular Varieties
12. Strictly Simple Algebras
13. Mal’cev Conditions for Lattice Equations
14. A Finite Basis Result
15. Pure Lattice Congruence Identities
Similar
Abstract Algebra
Books