Distributive lattice decompositions of semirings with a semilattice additive reduct

Bhuniya, A. K.; Mondal, Tapas Kumar

doi:10.1007/s00233-009-9205-6

Cited by 17 publications

(3 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [1], the Bourne regularity was renamed as k-regularity to distinguish it from von Neumann regularity. If S is a semiring in SL + , then S is k-regular if and only if for every a ∈ S there exists x ∈ S such that a + axa = axa, by Lemma 2.1 (2). Again we refer [12,13,15] as further references on k-regular semirings.…”

Section: Preliminariesmentioning

confidence: 99%

STRUCTURE AND SOME CHARACTERIZATIONS OF LEFT k-CLIFFORD SEMIRINGS

Bhuniya

2013

Asian-European J. Math.

Self Cite

View full text Add to dashboard Cite

Here, being motivated from the works of Zhu, Guo and Shum on left Clifford semigroups, we have introduced left k-Clifford semirings as a generalization of k-Clifford semirings. A k-regular semiring S ∈ SL + is a left k-Clifford semiring (left k-semifield) if for all a ∈ S, aS ⊆ Sa (for all b ∈ S , a ∈ Sb). Several characteristics for this class of semirings are obtained. Moreover a semiring is left k-Clifford if and only if it is a distributive lattice of left k-semifields.Keywords: k-regular semiring; left k-semifield; left k-Clifford semiring; distributive lattice of left k-semifields.

show abstract

Section: Preliminariesmentioning

confidence: 99%

STRUCTURE AND SOME CHARACTERIZATIONS OF LEFT k-CLIFFORD SEMIRINGS

Bhuniya

2013

Asian-European J. Math.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Indeed, there were some research articles on semirings, (see, for example, [8][9][10][11][12][13][14]), specially on the radical of a semiring; see [15][16][17][18]. Semigroups over semirings were studied in [19] and semimodules over semirings were studied in [14].…”

Section: Introductionmentioning

confidence: 99%

On the Jacobson Radical of an (m,n)-Semiring

Zhu

2013

Algebra

View full text Add to dashboard Cite

show abstract

“…While studying the structure of semigroups, semilattice decomposition of semigroups, an elegant technique, was first defined and studied by A.H. Clifford [9]. This motivates us to study on the structure of semirings whose additive reduct is a semilattice [3,4,5,14]. M.K.…”

Section: Introductionmentioning

confidence: 99%