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On the lattice of congruences on inverse semirings

100%
Bhuniya A., Bhuniya A.
Discussiones Mathematicae - General Algebra and Applications
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2008
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tom 28
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nr 2
193-208
EN
Let S be a semiring whose additive reduct (S,+) is an inverse semigroup. The relations θ and k, induced by tr and ker (resp.), are congruences on the lattice C(S) of all congruences on S. For ρ ∈ C(S), we have introduced four congruences $ρ_{min}, ρ_{max}, ρ^{min}$ and $ρ^{max}$ on S and showed that $ρθ = [ρ_{min},ρ_{max}]$ and $ρκ = [ρ^{min},ρ^{max}]$. Different properties of ρθ and ρκ have been considered here. A congruence ρ on S is a Clifford congruence if and only if $ρ_{max}$ is a distributive lattice congruence and $ρ^{max}$ is a skew-ring congruence on S. If η (σ) is the least distributive lattice (resp. skew-ring) congruence on S then η ∩ σ is the least Clifford congruence on S.
2
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On k-radicals of Green's relations in semirings with a semilattice additive reduct

100%
Mondal T., Bhuniya A.
Discussiones Mathematicae - General Algebra and Applications
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2013
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tom 33
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nr 1
85-93
EN
We introduce the k-radicals of Green's relations in semirings with a semilattice additive reduct, introduce the notion of left k-regular (right k-regular) semirings and characterize these semirings by k-radicals of Green's relations. We also characterize the semirings which are distributive lattices of left k-simple subsemirings by k-radicals of Green's relations.
3
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On the subsemigroup generated by ordered idempotents of a regular semigroup

100%
Bhuniya A., Kalyan Hansda K.
Discussiones Mathematicae - General Algebra and Applications
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2015
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tom 35
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nr 2
205-211
EN
An element $e$ of an ordered semigroup S is called an ordered idempotent if e ≤ e². Here we characterize the subsemigroup $$ generated by the set of all ordered idempotents of a regular ordered semigroup S. If S is a regular ordered semigroup then $$ is also regular. If S is a regular ordered semigroup generated by its ordered idempotents then every ideal of S is generated as a subsemigroup by ordered idempotents.
4
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Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct

100%
Bhuniya A., Jana K.
Discussiones Mathematicae - General Algebra and Applications
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2014
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tom 34
|
nr 1
27-43
EN
Here we introduce the notion of strong quasi k-ideals of a semiring in SL⁺ and characterize the semirings that are distributive lattices of t-k-simple(t-k-Archimedean) subsemirings by their strong quasi k-ideals. A quasi k-ideal Q is strong if it is an intersection of a left k-ideal and a right k-ideal. A semiring S in SL⁺ is a distributive lattice of t-k-simple semirings if and only if every strong quasi k-ideal is a completely semiprime k-ideal of S. Again S is a distributive lattice of t-k-Archimedean semirings if and only if √Q is a k-ideal, for every strong quasi k-ideal Q of S.
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