Residuation Theory aims to contribute to literature in the field of ordered algebraic
structures, especially on the subject of residual mappings. The book is divided into three …

This book introduces recently developed ideas and techniques in semigroup theory to
provide a handy reference guide previously unavailable in a single volume. The opening …

For example, the idempotents of an inverse semigroup form a semilattice. All isomorphisms
between principal ideals of a semilattice E form the Munn inverse semigroup T,, which …

Residuation is a fundamental concept of ordered structures and categories. In this survey we
consider the consequences of adding a residuated monoid operation to lattices. The …

A commutative residuated lattice, is an ordered algebraic structure, where (L,·, e) is a
commutative monoid,(L,∧,∨) is a lattice, and the operation→ satisfies the equivalences for …

0.1. General remarks. For any algebraic system A, the set SubA of all subsystems of A
partially ordered by inclusion forms a lattice. This is the subsystem lattice of A.(In certain …

Some of the very striking common features of Brouwerian Algebras and commutative 1-
groups are that (i) both are distributive lattices,(ii) both can be dually residuated and (iii) both …

1. Introduction. When studying ideal theory in semirings, it is natural to consider the quotient
structure of a semiring modulo an ideal. If I is an ideal in a semiring R, the collection {x+ I} …

A semiring (S,+,·) is a nonempty set S, endowed with associative operations of addition and
multiplication, such that the multiplicative semigroup (S,·) distributes over the addition. That …

A (meet-) semilattice is an algebra with one binary operation∧, which is associative,
commutative and idempotent. Throughout this paper we are working in the category of …