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

100%
Maity S.
Discussiones Mathematicae - General Algebra and Applications
|
2014
|
tom 34
|
nr 1
75-84
EN
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.
2
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Clifford congruences on generalized quasi-orthodox GV-semigroups

100%
Maity S.
Discussiones Mathematicae - General Algebra and Applications
|
2013
|
tom 33
|
nr 2
137-145
EN
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.
3
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Congruences on bands of π-groups

100%
Maity S.
Discussiones Mathematicae - General Algebra and Applications
|
2013
|
tom 33
|
nr 1
5-11
EN
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.
4
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Nil-extensions of completely simple semirings

64%
Maity S., Ghosh R.
Discussiones Mathematicae - General Algebra and Applications
|
2013
|
tom 33
|
nr 2
201-209
EN
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.
5
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Clifford semifields

51%
Sen M., Maity S., Shum K.-P.
Discussiones Mathematicae - General Algebra and Applications
|
2004
|
tom 24
|
nr 1
125-135
EN
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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