Description
Springer M-Solid Varieties Of Algebras by Joerg Koppitz , Klaus Denecke
A complete and systematic introduction to the fundamentals of the hyperequational theory of universal algebra, offering the newest results on solid varieties of semirings and semigroups. The book aims to develop the theory of solid varieties as a system of mathematical discourse that is applicable in several concrete situations. A unique feature of this book is the use of Galois connections to integrate different topics._x000D_ _x000D_Preface Chapter 1 _x000D_
Basic Concepts_x000D_
1.1 Subalgebras and Homomorphic Images_x000D_
1.2 Direct and Subdirect Products_x000D_
1.3 Term Algebras, Identities, Free Algebras_x000D_
1.4 The Galois Connection (Id,Mod) Chapter 2 _x000D_
Closure Operators and Lattices_x000D_
2.1 Closure Operators and Kernel Operators_x000D_
2.2 Complete Sublattices of a Complete Lattice_x000D_
2.3 Galois Connections and Complete Lattices_x000D_
2.4 Galois Closed Subrelations_x000D_
2.5 Conjugate Pairs of Additive Closure Operators Chapter 3 _x000D_
M-Hyperidentities and M-solid Varieties_x000D_
3.1 M-Hyperidentities_x000D_
3.2 The Closure Operators_x000D_
3.3 M-Solid Varieties and their Characterization_x000D_
3.4 Subvariety Lattices and Monoids of Hypersubstitutions_x000D_
3.5 Derivation of M-Hyperidentities Chapter 4 _x000D_
Hyperidentities and Clone Identities_x000D_
4.1 Menger Algebras of Rank n_x000D_
4.2 The Clone of a Variety Chapter 5 _x000D_
Solid Varieties of Arbitrary Type_x000D_
5.1 Rectangular Algebras_x000D_
5.2 Solid Chains Chapter 6 _x000D_
Monoids of Hypersubstitutions_x000D_
6.1 Basic Definitions_x000D_
6.2 Injective and Bijective Hypersubstitutions_x000D_
6.3 Finite Monoids of Hypersubstitutions of Type (2)_x000D_
6.4 The Monoid of all Hypersubstitutions of Type (2)_x000D_
6.5 Greens Relations on Hyp(2)_x000D_
6.6 Idempotents in Hyp(2, 2)_x000D_
6.7 The Order of Hypersubstitutions of Type (2, 2)_x000D_
6.8 Greens Relations in Hyp(n, n)_x000D_
6.9 The Monoid of Hypersubstitutions of Type (n)_x000D_
6.10 Left-Seminearrings of Hypersubstitutions Chapter 7 _x000D_
M-Solid Varieties of Semigroups_x000D_
7.1 Basic Concepts onM-Solid Varieties of Semigroups_x000D_
7.2 Regular-solid Varieties of Semigroups_x000D_
7.3 Solid Varieties of Semigroups_x000D_
7.4 Pre-solid Varieties of Semigroups_x000D_
7.5 Locally Finite and Finitely Based M-solid Varieties Chapter 8 _x000D_
M-solid Varieties of Semirings_x000D_
8.1 Necessary Conditions for Solid Varieties of Semirings_x000D_
8.2 The Minimal Solid Variety of Semirings_x000D_
8.3 The Greatest Solid Variety of Semirings_x000D_
8.4 The Lattice of all Solid Varieties of Semirings_x000D_
8.5 Generalization of Normalizations_x000D_
8.6 All Pre-solid Varieties of Semirings Bibliography Glossary Index_x000D_