Book ChapterDOI
\(\Gamma \)-Semigroups: A Survey
M. K. Sen,S. Chattopadhyay +1 more
- Vol. 174, pp 225-239
Reads0
Chats0
TLDR
A survey of some works published by different authors on the concept of gamma-semigroups can be found in this article, where the authors present a survey of the generalization of semigroups.Abstract:
The concept of \(\Gamma \)-semigroup is a generalization of semigroup. Let S and \(\Gamma \) be two nonempty sets. S is called \(\Gamma \)-semigroup if there exists a mapping \(S\times \Gamma \times S\longrightarrow S\), written as \((a, \alpha , b)\longrightarrow a\alpha b\), satisfying the identity \( (a\alpha b)\beta c\) \(=\) \(a\alpha (b\beta c) \) for all \(a, b, c\in S\) and \( \alpha , \beta \in \Gamma \). This article is a survey of some works published by different authors on \(\Gamma \)-semigroups.read more
Citations
More filters
Journal ArticleDOI
A Generalization of the Artin Theorem
Yu. M. Movsisyan,M. A. Yolchyan +1 more
TL;DR: In this paper, a wide generalization of the Artin theorem using the concepts of hyperidentity and co-identity is proposed, referred to as $$g$$¯¯¯¯ -algebras.
Journal ArticleDOI
Cayley-type theorems for $g$-dimonoids
TL;DR: In this article , the authors prove Cayley-type theorems for $g$-dimonoids using the left (right) acts of sets and concept of dialgebra.
References
More filters
Journal ArticleDOI
How to assign votes in a distributed system
TL;DR: In this article, the authors studied both of these strategies in detail and showed that they are not equivalent in general (although they are in some cases) and proved several interesting properties.
Journal ArticleDOI
On regular semigroups whose idempotents form a subsemigroup
TL;DR: In this article, the finest inverse semigroup congruence on an orthodox semigroup is shown to have a simple form and conversely, regular semigroups whose finest inverse congruences has this simple form are shown to be orthodox.
Journal ArticleDOI
Regular semi-groups whose idempotents satisfy permutation identities.
TL;DR: In this paper, a structure theorem for generalized inverse semigroups is established and some theorems are given to clarify the mutual relations between several conditions on semiigroups, including permutation identities.