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 A final remark on extending to strict total orders in modules

1973 ◽  
Vol 9 (1) ◽  
pp. 137-140 ◽  
Author(s):  
Isidore Fleischer
Keyword(s):  
Recent Work ◽  
Universal Algebra ◽  
Partially Ordered ◽  
Final Remark ◽  
Standard Order ◽  
Ordered Ring ◽  
Order Extension ◽  
Total Orders

The remark is that the recent work in this Bulletin dealing with the extension of a partial to a total strict order on a module over a partially ordered ring falls under standard order extension results for operator groups once it is noted that the added requirement of strictness just comes to injective operation of the positive scalars. These standard results are in turn generalized to a universal algebra setting.

ON AUTOMORPHISMS OF THE ENDOMORPHISM SEMIGROUP OF A FREE UNIVERSAL ALGEBRA

2007 ◽  
Vol 17 (05n06) ◽  
pp. 1085-1106 ◽  
Author(s):  
G. MASHEVITZKY ◽  
B. I. PLOTKIN
Keyword(s):  
Lie Algebras ◽  
Universal Algebra ◽  
Automorphism Groups ◽  
Endomorphism Semigroup ◽  
Universal Algebras ◽  
Free Lie Algebras ◽  
Inner Automorphism ◽  
Groups Of Automorphisms ◽  
Inner Automorphisms

Let U be a universal algebra. An automorphism α of the endomorphism semigroup of U defined by α(φ) = sφs-1 for a bijection s : U → U is called a quasi-inner automorphism. We characterize bijections on U defining such automorphisms. For this purpose, we introduce the notion of a pre-automorphism of U. In the case when U is a free universal algebra, the pre-automorphisms are precisely the well-known weak automorphisms of U. We also provide different characterizations of quasi-inner automorphisms of endomorphism semigroups of free universal algebras and reveal their structure. We apply obtained results for describing the structure of groups of automorphisms of categories of free universal algebras, isomorphisms between semigroups of endomorphisms of free universal algebras, automorphism groups of endomorphism semigroups of free Lie algebras etc.

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

L-fuzzy cosets in universal algebras

2021 ◽  
Vol 71 (3) ◽  
pp. 573-594
Author(s):  
Gezahagne Mulat Addis
Keyword(s):  
General Theory ◽  
Universal Algebra ◽  
Fuzzy Set ◽  
Fuzzy Systems ◽  
Algebraic Closure ◽  
Sufficient Conditions ◽  
General Context ◽  
Variety Of Algebras ◽  
Universal Algebras ◽  
Necessary And Sufficient

Abstract In this paper, we introduce the notion of fuzzy costs in a more general context, in universal algebra by the use of coset terms. We study the structure of fuzzy cosets by applying the general theory of algebraic fuzzy systems. Fuzzy cosets generated by a fuzzy set are characterized in different ways. It is also proved that the class of fuzzy cosets determined by an element forms an algebraic closure fuzzy set system. Finally, we give a set of necessary and sufficient conditions for a given variety of algebras to be congruence permutable by applying the theory of fuzzy cosets.

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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