M-Solid Varieties of Algebras

Preface Chapter 1 Basic Concepts1.1 Subalgebras and Homomorphic Images1.2 Direct and Subdirect Products1.3 Term Algebras, Identities, Free Algebras1.4 The Galois Connection (Id,Mod) Chapter 2 Closure Operators and Lattices2.1 Closure Operators and Kernel Operators2.2 Complete Sublattices of a Complete Lattice2.3 Galois Connections and Complete Lattices2.4 Galois Closed Subrelations2.5 Conjugate Pairs of Additive Closure Operators Chapter 3 M-Hyperidentities and M-solid Varieties3.1 M-Hyperidentities3.2 The Closure Operators3.3 M-Solid Varieties and their Characterization3.4 Subvariety Lattices and Monoids of Hypersubstitutions3.5 Derivation of M-Hyperidentities Chapter 4 Hyperidentities and Clone Identities4.1 Menger Algebras of Rank n4.2 The Clone of a Variety Chapter 5 Solid Varieties of Arbitrary Type5.1 Rectangular Algebras5.2 Solid Chains Chapter 6 Monoids of Hypersubstitutions6.1 Basic Definitions6.2 Injective and Bijective Hypersubstitutions6.3 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 Semigroups7.1 Basic Concepts on M-Solid Varieties of Semigroups7.2 Regular-solid Varieties of Semigroups7.3 Solid Varieties of Semigroups7.4 Pre-solid Varieties of Semigroups7.5 Locally Finite and Finitely Based M-solid Varieties Chapter 8 M-solid Varieties of Semirings8.1 Necessary Conditions for Solid Varieties of Semirings8.2 The Minimal Solid Variety of Semirings8.3 The Greatest Solid Variety of Semirings8.4 The Lattice of all Solid Varieties of Semirings8.5 Generalization of Normalizations8.6 All Pre-solid Varieties of Semirings Bibliography Glossary Index