منابع مشابه
Representable Semilattice-Ordered Monoids
We show that no finite set of first-order axioms can define the class of representable semilattice-ordered monoids.
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As Jonathan Leech has pointed out, many natural examples of inverse semigroups are semilattice ordered under the natural partial order. But there are many interesting examples of semilattice ordered inverse semigroups in which the imposed partial order is not the natural one. In this talk we shall explore the structure and properties of these examples and some other questions related to semilat...
متن کاملInverse Monoids with a Natural Semilattice Ordering
An inverse semigroup is a semigroup S such that for each x e S there exists a unique inverse x~ & S such that both xx~x=x and x~xx~=x~\ This condition is equivalent to S both being (von Neumann) regular and having all idempotents commute. The classic example of such a semigroup is the symmetric inverse semigroup Ix of all partial bijections on a set X under the standard composition of partial f...
متن کاملOn representable ordered residuated semigroups
We show that the equational theory of representable lattice-ordered residuated semigroups is not finitely axiomatizable. We apply this result to the problem of completeness of substructural logics.
متن کاملOrdered monoids and J-trivial monoids
In this paper we give a new proof of the following result of Straubing and Thérien: every J -trivial monoid is a quotient of an ordered monoid satisfying the identity x ≤ 1. We will assume in this paper that the reader has a basic background in finite semigroup theory (in particular, Green’s relations and identities defining varieties) and in computer science (languages, trees, heaps). All semi...
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ژورنال
عنوان ژورنال: Algebra universalis
سال: 2007
ISSN: 0002-5240,1420-8911
DOI: 10.1007/s00012-007-2055-8