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Congruences on bands of π-groups

Sunil K. Maity — 2013

Discussiones Mathematicae - General Algebra and Applications

A semigroup S is said to be completely π-regular if for any a ∈ S there exists a positive integer n such that aⁿ is completely regular. The present paper is devoted to the study of completely regular semigroup congruences on bands of π-groups.

On balanced order relations and the normal hull of completely simple semirings

Sunil K. Maity — 2014

Discussiones Mathematicae - General Algebra and Applications

In [1] the authors proved that a semiring S is a completely simple semiring if and only if S is isomorphic to a Rees matrix semiring over a skew-ring R with sandwich matrix P and index sets I and Λ which are bands under multiplication. In this paper we characterize all the balanced order relations on completely simple semirings. Also we study the normal hull of a completely simple semiring.

Clifford congruences on generalized quasi-orthodox GV-semigroups

Sunil K. Maity — 2013

Discussiones Mathematicae - General Algebra and Applications

A semigroup S is said to be completely π-regular if for any a ∈ S there exists a positive integer n such that aⁿ is completely regular. A completely π-regular semigroup S is said to be a GV-semigroup if all the regular elements of S are completely regular. The present paper is devoted to the study of generalized quasi-orthodox GV-semigroups and least Clifford congruences on them.

Nil-extensions of completely simple semirings

Sunil K. MaityRituparna Ghosh — 2013

Discussiones Mathematicae - General Algebra and Applications

A semiring S is said to be a quasi completely regular semiring if for any a ∈ S there exists a positive integer n such that na is completely regular. The present paper is devoted to the study of completely Archimedean semirings. We show that a semiring S is a completely Archimedean semiring if and only if it is a nil-extension of a completely simple semiring. This result extends the crucial structure theorem of completely Archimedean semigroup.

Clifford semifields

Mridul K. SenSunil K. MaityKar-Ping Shum — 2004

Discussiones Mathematicae - General Algebra and Applications

It is well known that a semigroup S is a Clifford semigroup if and only if S is a strong semilattice of groups. We have recently extended 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. In this paper, we introduce the notions of Clifford semidomain and Clifford semifield. Some structure theorems for these semirings are obtained.

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