M-Solid Varieties of Algebras

Preface

Chapter 1
Basic Concepts
1.1 Subalgebras and Homomorphic Images
1.2 Direct and Subdirect Products
1.3 Term Algebras, Identities, Free Algebras
1.4 The Galois Connection (Id,Mod)

Chapter 2
Closure Operators and Lattices
2.1 Closure Operators and Kernel Operators
2.2 Complete Sublattices of a Complete Lattice
2.3 Galois Connections and Complete Lattices
2.4 Galois Closed Subrelations
2.5 Conjugate Pairs of Additive Closure Operators

Chapter 3
M-Hyperidentities and M-solid Varieties
3.1 M-Hyperidentities
3.2 The Closure Operators
3.3 M-Solid Varieties and their Characterization
3.4 Subvariety Lattices and Monoids of Hypersubstitutions
3.5 Derivation of M-Hyperidentities

Chapter 4
Hyperidentities and Clone Identities
4.1 Menger Algebras of Rank n
4.2 The Clone of a Variety

Chapter 5
Solid Varieties of Arbitrary Type
5.1 Rectangular Algebras
5.2 Solid Chains

Chapter 6
Monoids of Hypersubstitutions
6.1 Basic Definitions
6.2 Injective and Bijective Hypersubstitutions
6.3 Finite Monoids of Hypersubstitutions of Type (2)
6.4 The Monoid of all Hypersubstitutions of Type (2)
6.5 Green’s Relations on Hyp(2)
6.6 Idempotents in Hyp(2, 2)
6.7 The Order of Hypersubstitutions of Type (2, 2)
6.8 Green’s Relations in Hyp(n, n)
6.9 The Monoid of Hypersubstitutions of Type (n)
6.10 Left-Seminearrings of Hypersubstitutions

Chapter 7
M-Solid Varieties of Semigroups
7.1 Basic Concepts on M-Solid Varieties of Semigroups
7.2 Regular-solid Varieties of Semigroups
7.3 Solid Varieties of Semigroups
7.4 Pre-solid Varieties of Semigroups
7.5 Locally Finite and Finitely Based M-solid Varieties

Chapter 8
M-solid Varieties of Semirings
8.1 Necessary Conditions for Solid Varieties of Semirings
8.2 The Minimal Solid Variety of Semirings
8.3 The Greatest Solid Variety of Semirings
8.4 The Lattice of all Solid Varieties of Semirings
8.5 Generalization of Normalizations
8.6 All Pre-solid Varieties of Semirings

Bibliography

Glossary

Index