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M. K. Sen

Bio: M. K. Sen is an academic researcher from University of Calcutta. The author has contributed to research in topics: Semiring & Semigroup. The author has an hindex of 3, co-authored 8 publications receiving 35 citations.

Papers
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Journal ArticleDOI
TL;DR: In this article, it was shown that a semiring $S$ is a Clifford semiring if and only if it is a strong distributive lattice of skew-rings.
Abstract: It is well known that a semigroup $S$ is a Clifford semigroup if and only if $S$ is a strong semilattice of groups. In this paper, we extend this important result from semigroups to semirings by showing that a semiring $S$ is a Clifford semiring if and only if $S$ is a strong distributive lattice of skew-rings. Also, as a further generalization, we prove that a semiring $S$ is a genneralized Clifford semiring if and only if $S$ is a strong b-lattice of skew-rings. Some results which have been recently obtained in the literature [2] are strengthened and extended.

19 citations

01 Jan 2006
TL;DR: In this article, it was shown that the sum of two principal left ideals is again a principal left ideal in a regular additively inverse semiring with 1 satisfying the conditions (A) a(a + a )= a + a; (B) a (b + b )=( b + b)a and (C) a + b + a(b+ b)= a, for all a,b ∈ S,
Abstract: In this paper we show that in a regular additively inverse semiring (S,+, ·) with 1 satisfying the conditions (A) a(a + a )= a + a; (B) a(b + b )=( b + b)a and (C) a + a(b + b )= a, for all a,b ∈ S, the sum of two principal left ideals is again a principal left ideal. Also, we decompose S as a direct sum of two mutually inverse ideals.

8 citations

01 Jan 2004
Abstract: We show in an additive inverse regular semiring (S, +, ·) with E•(S) as the set of all multiplicative idempotents and E(S) as the set of all additive idempotents, the following conditions are equivalent: (i) For all e, f ∈ E•(S), ef ∈ E(S) implies fe ∈ E(S). (ii) (S, ·) is orthodox. (iii) (S, ·) is a semilattice of groups. This result generalizes the corresponding result of regular ring.

5 citations

Journal ArticleDOI
TL;DR: In this article, the semidirect product of a semigroup and a Γ-semigroup is studied and some interesting properties of this product are investigated. And the notion of wreath product is introduced.
Abstract: 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. In this paper we study the semidirect product of a semigroup and a Γ-semigroup. We also introduce the notion of wreath product of a semigroup and a Γsemigroup and investigate some interesting properties of this product.

3 citations

Proceedings ArticleDOI
01 Jul 2003

1 citations


Cited by
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TL;DR: From the perspective of semigroup theory, the characterizations of a neutrosophic extended triplet group (NETG) and AG-NET-loop (which is both an Abel-Grassmann groupoid and a neutrosexual triplet loop) are systematically analyzed and some important results are obtained.
Abstract: From the perspective of semigroup theory, the characterizations of a neutrosophic extended triplet group (NETG) and AG-NET-loop (which is both an Abel-Grassmann groupoid and a neutrosophic extended triplet loop) are systematically analyzed and some important results are obtained. In particular, the following conclusions are strictly proved: (1) an algebraic system is neutrosophic extended triplet group if and only if it is a completely regular semigroup; (2) an algebraic system is weak commutative neutrosophic extended triplet group if and only if it is a Clifford semigroup; (3) for any element in an AG-NET-loop, its neutral element is unique and idempotent; (4) every AG-NET-loop is a completely regular and fully regular Abel-Grassmann groupoid (AG-groupoid), but the inverse is not true. Moreover, the constructing methods of NETGs (completely regular semigroups) are investigated, and the lists of some finite NETGs and AG-NET-loops are given.

30 citations

Journal ArticleDOI
TL;DR: In this article, when an additive mapping T on S becomes centralizer, a 2-torsion free semiprime inverse semiring satisfying A2 condition of Bandlet and Petrich is investigated.
Abstract: Let S be 2-torsion free semiprime inverse semiring satisfying A2 condition of Bandlet and Petrich [1]. We investigate, when an additive mapping T on S becomes centralizer.

17 citations

13 May 2013

16 citations

01 Jan 2012
TL;DR: In this paper, the notion of commutators for a certain class of semirings satisfying the condition (A2) of Bandlet and Petrich was introduced, and a few fundamental results of this class included Jacobian and other identities, that become special relevant cases of ring theory.
Abstract: In this paper, we introduce the notion of commutators for a certain class of semirings satisfying the condition (A2) of Bandlet and Petrich. We establish a few fundamental results of this class included Jacobian and other identities, that become special relevant cases of ring theory, and may be helpful to initiate Lie type theory of semirings (MAsemirings).

12 citations