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Skew Pairs of Idempotents in Transformation Semigroups

Acta Mathematica Sinica, English Series, 2006
An ordered pair (e, f) of idempotents of a regular semigroup is called a skew pair if ef is not idempotent whereas fe is idempotent. We have shown previously that there are four distinct types of skew pairs of idempotents.
T S Blyth, M H Almeida Santos, Blyth T S
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On Factorisations and Generators in Transformation Semigroups

Semigroup Forum, 2004
A cycle-style notation is introduced for members of the full transformation semigroup similar to that used by Lipscomb for partial one-to-one maps. This approach is used to study generating sets of the submonoids \(T_{n,r}\) of \(T_n\) consisting of the union of the symmetric group and the ideal of all mappings with range of cardinality no greater than
Ayik G., Ayik H., Howie J.M.
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A property of transformation semigroups

Semigroup Forum, 2012
Let \(S\) be a semigroup. For \(a,b\in S\) we write \(a\leq b\) if \(a=xb=by\) and \(xa=a\) for some \(x,y\in S^1\). The author calls \(S\) right (left) quasiresiduated if for any \(a,b\in S\) there exists \(x\in S\) such that \(ax\leq b\) (resp. \(xa\leq b\)). If \(S\) has a zero element it makes sense to require that all \(a,b\) and \(x\) are nonzero.
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On the Rank of Generalized Transformation Semigroups

Bulletin of the Malaysian Mathematical Sciences Society, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gonca Ayık, Haytham Darweesh Mustafa Abusarris   +1 more
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On some semigroups of the partial transformation semigroup

AIP Conference Proceedings, 2012
Finite semigroups arise as syntactic semigroups of regular languages and as transition semigroups of finite automata. Among the most important and intensively studied classes of finite semigroups are the partial transformation semigroup and the semigroup of all order-preserving partial transformations.
Ivan D. Trendafilov, Dimitrinka I. Vladeva   +1 more
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Factorisable Semigroups of Linear Transformations

Algebra Colloquium, 2006
Let P(X) be the semigroup of all partial transformations of a set X. A subsemigroup S of P(X) is factorisable if S = GE = EH, where G, H are subgroups of S and E is the set of idempotents in S. In 2001, Jampachon, Saichalee and Sullivan proved a simple result that generalized most of the previous work on factorisable subsemigroups of P(X).
Ittharat, Jirasook, Sullivan, R. P.
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On Groups Associated with Transformation Semigroups

SemiGroup Forum, 1999
Denote by \({\mathcal P}_n\) the semigroup of all partial transformations on a finite set \(X_n\). Denote by \(S_n\) the symmetric group of permutations of \(X_n\) and let \(S\) be any subsemigroup of \({\mathcal P}_n\). An automorphism \(\varphi\) of \(S\) is defined to be inner if there exists an \(h\in S_n\) such that \(\varphi(\alpha)=h\alpha h^{-1}
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Decompositions of -generalized transformation semigroups

Fuzzy Sets and Systems, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sung Jin Cho 0001, Jae-Gyeom Kim, Woon-Seek Lee   +2 more
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Comparison semigroups and algebras of transformations

Semigroup Forum, 2010
A set equipped with a certain quaternary comparison operation \((-,-)[-,-]\) is called a `comparison algebra'. A semigroup \((A,\cdot)\) equipped with a comparison operation \((-,-)[-,-]\) which satisfies the equalities \((a,b)[c,d]\cdot e=(a,b)[ce,de]\) and \(e\cdot(a,b)[c,d]=(ea,eb)[ec,ed]\) for all \(a,b,c,d,e\in A\), is called a `comparison ...
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REPRESENTATIONS OF SEMIGROUPS BY TRANSFORMATIONS AND THE CONGRUENCE LATTICE OF AN EVENTUALLY REGULAR SEMIGROUP

International Journal of Algebra and Computation, 1996
On any eventually regular semigroup S, congruences ν, μL, μR, μ, K, KL, KR, ζ are introduced which are the greatest congruences over: nil-extensions (n.e.) of completely simple semigroups, n.e. of left groups, n.e. of right groups, n.e. of groups, n.e. of rectangular bands, n.e. of left zero semigroups, n.e.
Karl Auinger, Thomas Eric Hall
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