scholarly journals On Morita equivalence of partially ordered semigroups with local units

2020 ◽  
Vol 15 (2) ◽  
pp. 15-33
Author(s):  
Lauri Tart
Keyword(s):  
Morita Equivalence ◽  
Morita Context ◽  
Ordered Semigroups ◽  
Partially Ordered

We show that for two partially ordered semigroups S and T with common local units, there exists a unitary Morita context with surjective maps if and only if the categories of closed right S- and T-posets are equivalent.

Characterizations of strong Morita equivalence for ordered semigroups with local units

2014 ◽  
Vol 64 (4) ◽  
Author(s):  
Lauri Tart
Keyword(s):  
Morita Equivalence ◽  
Ordered Semigroups ◽  
Local Isomorphism ◽  
Partially Ordered ◽  
Morita Equivalent ◽  
Strong Morita Equivalence

AbstractWe prove that partially ordered semigroups S and T with local units are strongly Morita equivalent if and only if there exists a surjective strict local isomorphism to T from a factorizable Rees matrix posemigroup over S. We also provide two similar descriptions which use Cauchy completions and Morita posemigroups instead.

Finiteness of Semigroups of Operators in Universal Algebra

1967 ◽  
Vol 19 ◽  
pp. 764-768 ◽  
Author(s):  
Evelyn Nelson
Keyword(s):  
Universal Algebra ◽  
Partial Solution ◽  
Semigroups Of Operators ◽  
Ordered Semigroups ◽  
Universal Algebras ◽  
Partially Ordered ◽  
Master's Thesis ◽  
Mcmaster University

This paper is a partial solution of problem 24 in (2) which suggests that the finiteness of the partially ordered semigroups generated by various combinations of operators on classes of universal algebras be investigated. The main result is that the semigroups generated by the following sets of operators (for definitions see §2) are finite: {H, S, P, Ps}, {C, H, S, P, PF} {C, H, S, PU, PF}.This paper is part of the author's Master's thesis written in the Department of Mathematics at McMaster University. The author is indebted to the referee for his helpful suggestions.

scholarly journals Acceptable Morita Contexts for Semigroups

ISRN Algebra ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Valdis Laan
Keyword(s):  
Short Note ◽  
Morita Equivalence ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Morita Context ◽  
Necessary And Sufficient

This short note deals with Morita equivalence of (arbitrary) semigroups. We give a necessary and sufficient condition for a Morita context containing two semigroups S and T to induce an equivalence between the category of closed right S-acts and the category of closed right T-acts.

scholarly journals Residuated Partially Ordered Semigroups

2007 ◽  
Vol 17 (7) ◽  
pp. 981-985
Author(s):  
Seok-Jong Lee ◽  
Yong-Chan Kim
Keyword(s):  
Ordered Semigroups ◽  
Partially Ordered

scholarly journals Morita equivalence for semigroups

1995 ◽  
Vol 59 (1) ◽  
pp. 81-111 ◽  
Author(s):  
S. Talwar
Keyword(s):  
Classical Theory ◽  
Morita Equivalence ◽  
Morita Context

AbstractIn this paper we shall extend the classical theory of Morita equivalence to semigroups with local units. We shall use the concept of a Morita context to rediscover the Rees theorem and to characterise completely 0-simple and regular bisimple semigroups.

On Partially Ordered Semigroups and an Abstract Set-Difference

2008 ◽  
Vol 16 (2-3) ◽  
pp. 257-265 ◽  
Author(s):  
D. Pallaschke ◽  
H. Przybycień ◽  
R. Urbański
Keyword(s):  
Ordered Semigroups ◽  
Partially Ordered

scholarly journals Proper Dubreil-Jacotin inverse semigroups

1975 ◽  
Vol 16 (1) ◽  
pp. 40-51 ◽  
Author(s):  
R. McFadden
Keyword(s):  
Inverse Semigroup ◽  
Algebraic Structure ◽  
Inverse Semigroups ◽  
Partial Ordering ◽  
Group Congruence ◽  
Complete Class ◽  
Ordered Semigroups ◽  
Partially Ordered ◽  
Minimum Group ◽  
Integrally Closed

This paper is concerned mainly with the structure of inverse semigroups which have a partial ordering defined on them in addition to their natural partial ordering. However, we include some results on partially ordered semigroups which are of interest in themselves. Some recent information [1, 2, 6, 7,11] has been obtained about the algebraic structure of partially ordered semigroups, and we add here to the list by showing in Section 1 that every regular integrally closed semigroup is an inverse semigroup. In fact it is a proper inverse semigroup [10], that is, one in which the idempotents form a complete class modulo the minimum group congruence, and the structure of these semigroups is explicitly known [5].

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