The concept of Γ-semigroup is a generalization of semigroup. Let S and _ be two nonempty sets. S is called Γ-semigroup if there exists a mapping S × Γ × S → S, written as (a, α, b) → aαb, satisfying the identity (aαb)βc = aα(bβc) for all a, b, c ∈ S and α, β ∈ Γ. This article is a survey of some works published by different authors on Γ-semigroups. © Springer Science+Business Media Singapore 2016.

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S CHATTOPADHYAY

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

\(\Gamma \)-Semigroups: A Survey

Springer Proceedings in Mathematics and Statistics

Let S = {a, b, c, ...} and Γ = {α, β, γ, ...} be two nonempty sets. S is called a Γ-semigroup if aαb ∈ S, for all α ∈ Γ and a, b ∈ S and (aαb)βc = aα(bβc), for all a, b, c ∈ S and for all α, β ∈ Γ. An element e ∈ S is said to be an α-idempotent for some α E Γ if eαe = e. A Γ-semigroup S is called an E-inversive Γ-semigroup if for each a ∈ S there exist x ∈ S and α ∈ Γ such that aαx is a β-idempotent for some β E Γ. A Γ-semigroup is called a right E-Γ-semigroup if for each α-idempotent e and β-idempotent f, eαf is a β-idempotent. In this paper we investigate different properties of E-inversive Γ-semigroup and right E-Γ-semigroup.

Kyungpook Mathematical Journal

E-inversive Î“-semigroups

In this paper we introduce the concept of [formula omitted]-regular, normal subset of a [formula omitted]-regular semigroup, give an alternate characterisation of the maximum idempotent separating congruence in a [formula omitted]-regular semigroup and finally describe the lattice of the idempotent separating congruences in a [formula omitted]-regular semigroup. © 1992, Australian Mathematical Society. All rights reserved.

Fulltext

Bulletin of the Australian Mathematical Society

Lattice of idempotent separating congruences in a [formula omitted]-regular semigroup

In this paper a Γ-group congruence on a regular Γ-semigroup is defined, some equivalent expressions for any Γ-group congruence on a regular Γ-semigroup and those for the least Γ-group congruence in particular are given. © 1992, Hindawi Publishing Corporation. All rights reserved.

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ISSN	2194-1009