Distributive lattices of t-k-Archimedean semirings

Tapas Kumar Mondal

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...

A structure theory for a class of lattice ordered semirings

F. Smith (1966)

Fundamenta Mathematicae

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The greatest Archimedean ideal in a semigroup

František Kmeť (1987)

Mathematica Slovaca

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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 $\hat{C}$ -radicals. In addition, a necessary and sufficient condition...

On simply ordered groups

Michiura, Tadashi (1951)

Portugaliae mathematica

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On the distributive radical of an Archimedean lattice-ordered group

Ján Jakubík (2009)

Czechoslovak Mathematical Journal

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Let $G$ be an Archimedean $ℓ$ -group. We denote by $G^{d}$ and $R_{D} (G)$ the divisible hull of $G$ and the distributive radical of $G$ , respectively. In the present note we prove the relation ${(R_{D} (G))}^{d} = R_{D} (G^{d})$ . As an application, we show that if $G$ is Archimedean, then it is completely distributive if and only if it can be regularly embedded into a completely distributive vector lattice.