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

In [11], the author introduced inverse semimodules. Recently, in [8], we further studied properties of inverse semimodules and Clifford semimodules. In this paper, we consider inverse semimodules over a semiring R such that R is a distributive lattice of rings. In [3], the authors introduced von Neumann regular module and studied its properties. In this paper, we introduce von Neumann regular semimodule and study its different interesting properties. © 2021 Sciendo. All rights reserved.

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Pure Mathematics

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Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica

Von Neumann regular semimodule

The author [S. M. Yusuf, Inverse semimodules, J. Natur. Sci. Math. 6 (1966) 111-117.] introduced inverse semimodules. In this paper, we introduce Clifford semimodules. The Clifford semimodules have been characterized here as a strong R-semilattice of R-modules. The congruences on inverse semimodules, specially, the R-module congruences, have been characterized here completely. © 2021 World Scientific Publishing Company.

Asian-European Journal of Mathematics

Inverse semimodules

Semigroup Forum

Congruences on quasi completely regular semirings

In this article, we establish necessary and sufficient condition on a topological Clifford semigroup to be a semilattice of topological groups. As a consequence, we show that a topological Clifford semigroup (Formula presented.) satisfies the property that for each (Formula presented.) and every (Formula presented.) there exists an element (Formula presented.) such that (Formula presented.) if and only if it is a strong semilattice of topological groups if and only if it is a semilattice of topological groups. We prove that some topological properties like (Formula presented.) regularity and completely regularity are equivalent in a semilattice of topological groups. We also prove that the quotient space of a semilattice of topological groups by a full normal Clifford subsemigroup is again a semilattice of topological groups. Finally, we establish that if (Formula presented.) is a family of semilattices of topological groups and Ni is a full normal Clifford subsemigroup of Si for all (Formula presented.) then (Formula presented.) is topologically isomorphic to (Formula presented.). © 2021 Taylor & Francis Group, LLC.

Communications in Algebra

Semilattice of topological groups

A semiring (S, +,⋅) is said to be a quasi-orthodox semiring if for any e,f E+(S), there exists some positive integer n such that n(e + f) = (n + 1)(e + f). In this paper, we investigate the congruence generated by on quasi completely regular semirings with and without the special conditions like being quasi-orthodox. We further establish that the interval which - belongs to is [,ν]. © 2022 World Scientific Publishing Company.

The congruence y * on quasi completely regular semirings

Let S be a nil-extension of a b-lattice of skew-rings K by a semiring Q. A congruence pair (δ, ω) on S consists of a congruence δ on Q and a congruence ω on K. In this paper, we establish that there is an order preserving bijection between the set of all congruences on S onto the set of all congruence pairs on S. It is also proved that if S is a nil-extension of a completely regular semiring, then every congruence on S can be uniquely represented by a congruence pair and there is an order preserving bijection from the set of all congruences on S onto the set of all congruence pairs on S. © 2019, Institute of Mathematics, Academy of Sciences Moldova. All rights reserved.

Quasigroups and Related Systems

Congruences on nil-extension of a b-lattice of skew-rings

In this article, we define the Leavitt path algebra L S (Γ) of a directed graph Γ with coefficients in a Clifford semifield S. The general properties of L S (Γ) are briefly discussed. Then, concentrating on the full k-simplicity (that is, the property of having no nontrivial full k-ideals), we find the necessary and sufficient condition for full k-simplicity of L S (Γ) of a directed graph Γ over a Clifford semifield S. Also, we introduce c-homomorphisms of Leavitt path algebras over Clifford semifields and establish a version of the (Cuntz-Krieger) Uniqueness theorem for the Clifford semifield setting. © 2019, © 2019 Taylor & Francis Group, LLC.

GENERAL

Leavitt path algebras with coefficients in a Clifford semifield

Every quasi completely regular semiring is a b-lattice of completely Archimedean semirings, i.e., a b-lattice of nil-extensions of completely simple semirings. In this paper we consider the semiring which is a b-lattice of nil-extensions of orthodox completely simple semirings. © 2019, Institute of Mathematics, Academy of Sciences Moldova. All rights reserved.

B-lattice of nil-extensions of rectangular skew-rings

In this paper we investigate $${{\fancyscript{Y}}}^{*}$$Y∗, the congruence generated by $${\fancyscript{Y}}$$Y on GV-semigroups and finally prove that $${{\fancyscript{Y}}}^{*} \in [\epsilon , \nu ]$$Y∗∈[ϵ,ν] on GV-semigroups. © 2014, African Mathematical Union and Springer-Verlag Berlin Heidelberg.

Afrika Matematika

The congruence Y∗ on GV-semigroups

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.

Acta Mathematica Universitatis Comenianae

Regular additively inverse semirings

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.