Arithmetic properties of certain partially ordered semigroups

1975 ◽  
Vol 11 (1) ◽  
pp. 115-129 ◽  
Author(s):  
R. S. Pierce
Keyword(s):  
Ordered Semigroups ◽  
Partially Ordered ◽  
Arithmetic Properties

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 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

Arithmetic Properties Of Freely α-Generated Lattices

1962 ◽  
Vol 14 ◽  
pp. 476-481 ◽  
Author(s):  
Bjarni Jónsson
Keyword(s):  
Partially Ordered Set ◽  
Ordered Set ◽  
Canonical Representation ◽  
Free Lattice ◽  
Partially Ordered ◽  
Binary Operations ◽  
Arithmetic Properties ◽  
Irreducible Elements

In § 1 we give a characterization of a lattice L that is freely α-generated by a given partially ordered set P. In § 2 we obtain a representation of an element of such a lattice as a sum (product) of additively (multiplicatively) irreducible elements which, although not unique, has some of the desirable features of the canonical representation, in Whitman (2), of an element of a free lattice. The usefulness of this representation is illustrated in § 3, where some further arithmetic properties of these lattices are derived.We use + and . for the binary operations of lattice addition and multiplication, and Σ and II for the corresponding operations on arbitrary sets and sequences of lattice elements. In other respects the terminology will be the same as in Crawley and Dean (1).

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].

On partially ordered semigroups of relations with domino operations

2015 ◽  
Vol 92 (1) ◽  
pp. 198-213 ◽  
Author(s):  
Dmitry Aleksandrovich Bredikhin
Keyword(s):  
Ordered Semigroups ◽  
Partially Ordered

Completions for partially ordered semigroups

1986 ◽  
Vol 34 (1) ◽  
pp. 253-285 ◽  
Author(s):  
M. Erné ◽  
J. Z. Reichman
Keyword(s):  
Ordered Semigroups ◽  
Partially Ordered

Precoherent quantale completions of partially ordered semigroups

2019 ◽  
Vol 100 (2) ◽  
pp. 617-633
Author(s):  
Bin Zhao ◽  
Changchun Xia
Keyword(s):  
Ordered Semigroups ◽  
Partially Ordered
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