Distributive Lattices of -simple Semirings

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Kumar Mondal Tapas

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Journal Paper

Paper Information

Journal: IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS Year:2022 | Volume:17 | Issue:1 Page(s): 47-55

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Information Journal Paper

Title

Distributive Lattices of -simple Semirings

Author(s)

Kumar Mondal Tapas | Issue Writer Certificate

Keywords

Principal left k

radical

Distributive lattice congruence

Com

pletely semiprime k

ideal

simple semiring

Distributive lattice decomposi

tion

Abstract

In this paper, we study the decomposition of semirings with a semilattice additive reduct. For, we introduce the notion of principal left k-radicals (a) = fx 2 S j a l 􀀀 ! 1 xg induced by the transitive closure l 􀀀 ! 1 of the relation l 􀀀 ! which induce the equivalence relation . Again non-transitivity of l 􀀀 ! yields an expanding family f l 􀀀 ! ng of binary relations which associate subsets n(a) for all a 2 S, which again induces an equivalence relation n. We also de ne ( n)-simple semirings, and characterize the semirings which are distributive lattices of ( n)-simple semirings.

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APA: Copy

Kumar Mondal, Tapas. (2022). Distributive Lattices of -simple Semirings. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), 17(1), 47-55. SID. https://sid.ir/paper/990070/en

Vancouver: Copy

Kumar Mondal Tapas. Distributive Lattices of -simple Semirings. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)[Internet]. 2022;17(1):47-55. Available from: https://sid.ir/paper/990070/en

IEEE: Copy

Tapas Kumar Mondal, “Distributive Lattices of -simple Semirings,” IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), vol. 17, no. 1, pp. 47–55, 2022, [Online]. Available: https://sid.ir/paper/990070/en

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