Results 1 to 10 of about 166 (145)
Soft ideals of soft ternary semigroups [PDF]
Heliyon, 2021 In this paper, we introduce the notions of certain classes of soft ideals in soft ternary semigroups and study some inter-relations between different types of soft ideals in a soft ternary semigroup.
S. Kar, I. Dutta
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Lattices of completely regular semigroup varieties [PDF]
Pacific Journal of Mathematics, 1985 Let S be a regular semigroup, E(S) its set of idempotents, \({\mathcal C}(S)\) its congruence lattice. For \(\rho\in {\mathcal C}(S)\), the kernel and the trace of \(\rho\) is defined by ker \(\rho\) \(=\{x\in S\); \(x\rho\) e for \(e\in E(S)\}\), tr \(\rho\) \(=\rho | E(S)\). The sets \(T_{\rho}=\{\theta \in {\mathcal C}(S)\); tr \(\rho\) \(=tr \theta
Francis Pastijn
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The Kernel Relation for a Completely Regular Semigroup
Journal of Algebra, 1995 The kernel of a congruence \(\rho\) on a regular semigroup \(S\) is the union of the idempotent \(\rho\)-classes. The kernel relation \(K\) is the equivalence relation on the congruence lattice \(C(S)\) of \(S\) that identifies those congruences with the same kernel. This relation was introduced by \textit{F. Pastijn} and the author [Trans. Am.
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A semilattice of varieties of completely regular semigroups [PDF]
Mathematica Bohemica, 2020 Completely regular semigroups are unions of their (maximal) subgroups with the unary operation within their maximal subgroups. As such they form a variety whose lattice of subvarieties is denoted by $\mathcal L(\mathcal C\mathcal R)$.
Mario Petrich
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Relations on a lattice of varieties of completely regular semigroups [PDF]
Mathematica Bohemica, 2020 Completely regular semigroups $\mathcal{CR}$ are considered here with the unary operation of inversion within the maximal subgroups of the semigroup. This makes $\mathcal{CR}$ a variety; its lattice of subvarieties is denoted by $\mathcal{L(CR)}$.
Mario Petrich
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Left (Right) Regular and Transposition Regular Semigroups and Their Structures
Mathematics, 2022 Regular semigroups and their structures are the most wonderful part of semigroup theory, and the contents are very rich. In order to explore more regular semigroups, this paper extends the relevant classical conclusions from a new perspective: by ...
Xiaohong Zhang, Yudan Du
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From ∨e-Semigroups to Hypersemigroups
Discussiones Mathematicae - General Algebra and Applications, 2021 A poe-semigroup is a semigroup S at the same time an ordered set having a greatest element “e” in which the multiplication is compatible with the ordering.
Kehayopulu Niovi
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Some ordered hypersemigroups which enter their properties into their σ-classes [PDF]
Journal of Hyperstructures, 2017 An important problem in the theory of ordered hypersemigroups is to describe the ordered hypersemigroups which enter their properties into their σ-classes.
Niovi Kehayopulu
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Some results on semigroups of transformations with restricted range
Open Mathematics, 2021 Let XX be a non-empty set and YY a non-empty subset of XX. Denote the full transformation semigroup on XX by T(X)T\left(X) and write f(X)={f(x)∣x∈X}f\left(X)=\{f\left(x)| x\in X\} for each f∈T(X)f\in T\left(X). It is well known that T(X,Y)={f∈T(X)∣f(X)⊆Y}
Yan Qingfu, Wang Shoufeng
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A NOTE ON PSEUDOVARIETIES OF COMPLETELY REGULAR SEMIGROUPS [PDF]
Bulletin of the Australian Mathematical Society, 2015 A paper of Almeida and Trotter [‘The pseudoidentity problem and reducibility for completely regular semigroups’, Bull. Aust. Math. Soc.63 (2001), 407–433] makes essential use of free profinite semigroupoids over profinite graphs with infinitely many vertices. It has since been shown that such structures must be handled with great care. In this note, it
Almeida, Jorge, Costa, Alfredo
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