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Strong quasi k-ideals and the lattice decompositions of semirings with semilattice additive reduct

Anjan Kumar BhuniyaKanchan Jana — 2014

Discussiones Mathematicae - General Algebra and Applications

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...

On k-radicals of Green's relations in semirings with a semilattice additive reduct

Tapas Kumar MondalAnjan Kumar Bhuniya — 2013

Discussiones Mathematicae - General Algebra and Applications

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.

On the subsemigroup generated by ordered idempotents of a regular semigroup

Anjan Kumar BhuniyaKalyan Hansda — 2015

Discussiones Mathematicae - General Algebra and Applications

An element e of an ordered semigroup S is called an ordered idempotent if e ≤ e². Here we characterize the subsemigroup g e n e r a t e d b y t h e s e t o f a l l o r d e r e d i d e m p o t e n t s o f a r e g u l a r o r d e r e d s e m i g r o u p S . I f S i s a r e g u l a r o r d e r e d s e m i g r o u p t h e n 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.

On the lattice of congruences on inverse semirings

Anwesha BhuniyaAnjan Kumar Bhuniya — 2008

Discussiones Mathematicae - General Algebra and Applications

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 m i n , ρ m a x , ρ m i n and ρ m a x on S and showed that ρ θ = [ ρ m i n , ρ m a x ] and ρ κ = [ ρ m i n , ρ m a x ] . Different properties of ρθ and ρκ have been considered here. A congruence ρ on S is a Clifford congruence if and only if ρ m a x is a distributive lattice congruence and ρ m a x is a skew-ring congruence on S. If η (σ) is the least distributive...

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