M. K. Sen

Bio: M. K. Sen is an academic researcher from University of Calcutta. The author has an hindex of 1, co-authored 1 publications receiving 1 citations.

\(\Gamma \)-Semigroups: A Survey

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.

A Generalization of the Artin Theorem

Abstract: The following Artin theorem about alternative linear algebras defined on the commutative, associative ring with unity is well-known: in an alternative linear algebra, if $$(a,b,c)=0$$ , then the subalgebra generated by the elements $$a$$ , $$b$$ , and $$c$$ is associative. In this paper a wide generalization of this classical result is proposed using the concepts of hyperidentity and coidentity. The corresponding universal algebras are referred to as $$g$$ -algebras.

Cayley-type theorems for $g$-dimonoids

Abstract: In this paper we prove Cayley-type theorems for $g$-dimonoids using the left (right) acts of sets and concept of dialgebra.