Results 121 to 130 of about 181 (150)

Equations Over Completely Simple Semigroups

Algebra and Logic, 2015
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On the rank of completely 0-simple semigroups

Mathematical Proceedings of the Cambridge Philosophical Society, 1994
AbstractConnected completely 0-simple semigroups are defined by a number of equivalent conditions, and a formula for the rank of these semigroups is proved. As a consequence an alternative proof of the result from [11] is given. In the case of a Rees matrix semigroupM0[G, I, Λ, P] the rank is expressed in terms of |I|, |Λ|,Gand a certain subgroup ...
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On completely simple semigroups.

2012
Summary: Completely simple semigroups or generalized groups are considered. We characterize generalized groups which are normal generalized groups. Homomorphisms of generalized groups are considered. Equivalent conditions for the kernel of a homomorphism are deduced.
Fatehi, F., Molaei, M. R.
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Residuated Completely Simple Semigroups

Algebra Colloquium, 2014
We consider particular compatible orders on a given completely simple semigroup Sx=M(〈x〉; I ,Λ;P) where 〈x〉 is an ordered cyclic group with x > 1 and P11=x-1. Of these, only the lexicographic and bootlace orders yield residuated semigroups. With the lexicographic order, Sx is orthodox and has a biggest idempotent.
T. S. Blyth, G. A. Pinto
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Completely simple and inverse semigroups

Mathematical Proceedings of the Cambridge Philosophical Society, 1961
The purpose of this paper is to investigate the structure of certain types of semigroups. Rees(6),(7) has determined the structure of a completely simple semigroup, and has shown that such a system may be realized as a type of matrix semigroup. Clifford (2) and Schwarz (8) have found conditions, namely, the existence of minimal left and minimal right ...
McFadden, R., Schneider, Hans
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ON ORDERED COMPLETELY SIMPLE SEMIGROUPS

Communications in Algebra, 2001
We consider an ordered completely simple semigroup S = M(G; I, Λ; P) which is non-degenerate in the sense that G, I, Λ are non-trivial. We prove that if every element of S has a biggest inverse then S contains at least one of seven particular types of subsemigroup.
T. S. Blyth, G. A. Pinto
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Counting completely 0-simple and completely simple semigroups

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1978
SynopsisFormulae are derived for the numbers of completely 0-simple and completely simple semigroups with m ℒ-classes, n ℜ-classes and underlying finite group G.
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Congruence-Simple Acts Over Completely Simple Semigroups

Journal of Mathematical Sciences
The authors investigate the conditions under which an act \(X\) over a completely simple semigroup \(S = M(G, I, \Lambda, P)\) is congruence-simple, meaning it has no non-trivial congruences. They identify four specific conditions that characterize such acts. The paper also provides a detailed description of these congruences.
Kozhukhov, I. B., Kolesnikova, K. A.
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Algebraic Geometry Over Completely Simple Semigroups

Algebra and Logic, 2016
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Extensions of Completely 0-Simple Semigroups by Completely 0-Simple Semigroups

Proceedings of the American Mathematical Society, 1966
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