Ebook: Lattices and Ordered Algebraic Structures

Ordered sets; residuated mappings -- Lattices; lattice morphisms -- Regular equivalences -- Modular lattices -- Distributive lattices -- Complementation; boolean algebras -- Pseudocomplementation; Stone and Heyting algebras -- Congruences; subdirectly irreducible algebras -- Ordered groups -- Archimedean ordered structures -- Ordered semigroups; residuated semigroups -- Epimorphic group images; Dubreil-Jacotin semigroups -- Ordered regular semigroups -- Structure theorems.;Provides a concise introduction to the theory of ordered sets and basic ordered algebraic structures. This book discusses the developments in the theory of residuated lattices and ordered regular semigroups. It presents an account of the range of applications of the theory, with illustrative examples and numerous exercises.