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Abundance of the semigroup of all transformations of a set that reflect an equivalence relation
Lei Sun,Limin Wang +1 more
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In this article, it was shown that the full transformation semigroup T ∃(X) is not abundant if X/E is infinite, and the semigroup is a subsemigroup of.Abstract:
Let be the full transformation semigroup on a nonempty set X and E be an equivalence relation on X. We write Then T∃(X) is a subsemigroup of . In this paper, we proved that the semigroup T∃(X) is not abundant if X/E is infinite.read more
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On certain semigroups of full contraction maps of a finite chain
TL;DR: In this article, the authors presented characterisations of Green's relations on both the CT and OCT subsemigroups of contraction maps and order-preserving contraction maps in the full transformation semigroup.
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Abundance of E-order-preserving transformation semigroups
Lei Sun,Xuefeng Han +1 more
TL;DR: In this article, a necessary and sufficient condition under which the semigroup EOPX is abundant is presented, and a subsemigroup of the full transformation semigroup is considered.
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Variant of finite symmetric inverse semigroup
TL;DR: In this paper, the authors studied the variant of the semigroup of Green's relations in the form of a symmetric inverse semigroup and showed that the variant semigroup is abundant.
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A new characterization of fuzzy ideals of semigroups and its applications
TL;DR: In this paper, a new technique for constructing fuzzy ideals of a semigroup was developed by using generalized Green's relations, and fuzzy star ideals were constructed by using fuzzy star relations.
References
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Fundamentals of semigroup theory
TL;DR: Inverse semigroups as discussed by the authors are a subclass of regular semigroup classes and can be seen as semigroup amalgamations of semigroup groups, which is a special case of regular semiigroups.
Journal ArticleDOI
Semigroups of transformations preserving an equivalence relation and a cross-section
João Araújo,Janusz Konieczny +1 more
TL;DR: In this article, a semigroup T(X, ρ, R) consisting of all mappings a from X to X such that a preserves both ρ and R is defined.
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On the semigroups of order-decreasing finite full transformations
TL;DR: In this paper, it was shown that Singn is a non-regular abundant semigroup with n − 1 -classes and is idempotent generated by the n(n − 1)/2 idempots in J*n−1.
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Abundant Semigroups of Transformations Preserving an Equivalence Relation
Huisheng Pei,Huijuan Zhou +1 more
TL;DR: In this article, the equivalence relations E so that the semigroup TE(X) is abundant are described, where E is a subsemigroup of the full transformation semigroup on X and E is an equivalence relation on X.
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Centralizers in the semigroup of injective transformations on an infinite set
TL;DR: For an infinite set X, the semigroup of all injective mappings from X to X is defined in this paper, and the elements of C(α) and Green's relations are characterized.