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Displaying similar documents to “Distributive lattices of t-k-Archimedean semirings”

Nil-extensions of completely simple semirings

Sunil K. Maity, Rituparna Ghosh (2013)

Discussiones Mathematicae - General Algebra and Applications

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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.

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

Anjan Kumar Bhuniya, Kanchan Jana (2014)

Discussiones Mathematicae - General Algebra and Applications

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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...

Some remarks on partitioning semirings.

Ebrahimi Atani, Shahabaddin, Ebrahimi Atani, Reza (2010)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

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Remarks on special ideals in lattices

Ladislav Beran (1994)

Commentationes Mathematicae Universitatis Carolinae

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The author studies some characteristic properties of semiprime ideals. The semiprimeness is also used to characterize distributive and modular lattices. Prime ideals are described as the meet-irreducible semiprime ideals. In relatively complemented lattices they are characterized as the maximal semiprime ideals. D -radicals of ideals are introduced and investigated. In particular, the prime radicals are determined by means of C ^ -radicals. In addition, a necessary and sufficient condition...