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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1179,
author = {Tapas Kumar Mondal},
title = {Distributive lattices of t-k-Archimedean semirings},
journal = {Discussiones Mathematicae - General Algebra and Applications},
volume = {31},
year = {2011},
pages = {147-158},
zbl = {1254.16042},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1179}
}
Tapas Kumar Mondal. Distributive lattices of t-k-Archimedean semirings. Discussiones Mathematicae - General Algebra and Applications, Tome 31 (2011) pp. 147-158. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1179/
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