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Distributive lattices of t-k-Archimedean semirings

Tapas Kumar Mondal — 2011

Discussiones Mathematicae - General Algebra and Applications

A semiring S in 𝕊𝕃⁺ is a t-k-Archimedean semiring if for all a,b ∈ S, b ∈ √(Sa) ∩ √(aS). Here we introduce the t-k-Archimedean semirings and characterize the semirings which are distributive lattice (chain) of t-k-Archimedean semirings. A semiring S is a distributive lattice of t-k-Archimedean semirings if and only if √B is a k-ideal, and S is a chain of t-k-Archimedean semirings if and only if √B is a completely prime k-ideal, for every k-bi-ideal B of S.

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

Tapas Kumar Mondal;  Anjan 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.

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