Results 141 to 150 of about 206 (177)
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Transformation Semigroups for Rough Sets
Lecture Notes in Computer Science, 2018In this article we define transformation semigroups for rough sets. Basic constructions such as closures, products, coverings and partitions for transformation semigroups are defined. A decomposition theorem for reset transformation semigroups is given. A connection with automata is also presented by defining a semiautomaton for rough sets.
Mohua Banerjee +2 more
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On Factorisations and Generators in Transformation Semigroups
Semigroup Forum, 2004A 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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ISOMORPHISM PROBLEMS FOR TRANSFORMATION SEMIGROUPS
Semigroups and Formal Languages, 2007 Many people have studied the problem of describing all isomorphisms between transformation semigroups dened on sets and between linear transformation semigroups dened on vector spaces. In this paper, we summarise some of that work, as well as recent work showing that Baer-Levi semigroups dened on sets are never isomorphic to their linear analogue ...
Suzana Mendes-Gonçalves
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On the Rank of Generalized Transformation Semigroups
Bulletin of the Malaysian Mathematical Sciences Society, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gonca Ayık +1 more
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A property of transformation semigroups
Semigroup Forum, 2012Let \(S\) 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 some semigroups of the partial transformation semigroup
AIP Conference Proceedings, 2012Finite 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 +1 more
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Factorisable Semigroups of Linear Transformations
Algebra Colloquium, 2006Let 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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Locally Factorisable Transformation Semigroups
Southeast Asian Bulletin of Mathematics, 2001A semigroup \(S\) is called factorizable if \(S=GE=EG\) where \(G\) is a subgroup of \(S\) and \(E\) is its set of idempotents; \(S\) is locally factorizable if \(eSe\) is factorizable for every idempotent \(e\). Suppose \(S\) is a subsemigroup of the partial transformation semigroup \(P(X)\) with identity \(\varepsilon\).
Jampachon, Prakit +2 more
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Set products in transformation semigroups
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2003We describe products of arbitrary L-, R- and H-classes with the set of idempotents of full transformation semigroups.
Higgins, Peter M. +2 more
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