Volume 17, Issue 1 (4-2022)                   IJMSI 2022, 17(1): 47-55 | Back to browse issues page

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Mondal T. Distributive Lattices of λ-simple Semirings. IJMSI. 2022; 17 (1) :47-55
URL: http://ijmsi.ir/article-1-1320-en.html
In this paper, we study the decomposition of semirings with a semilattice additive reduct. For, we introduce the notion of principal left $k$-radicals $Lambda(a)={x in S | a stackrel{l}{longrightarrow^{infty}} x}$ induced by the transitive closure $stackrel{l}{longrightarrow^{infty}}$ of the relation $stackrel{l}{longrightarrow}$ which induce the equivalence relation $lambda$. Again non-transitivity of $stackrel{l}{longrightarrow}$ yields an expanding family {$stackrel{l}{longrightarrow^n}}$ of binary relations which associate subsets $Lambda_n(a)$ for all $a in S$, which again induces an equivalence relation $lambda_n$. We also define $lambda(lambda_n)$-simple semirings, and characterize the semirings which are distributive lattices of $lambda(lambda_n)$-simple semirings.
Type of Study: Research paper | Subject: General

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