TY - JOUR
JF - IJMSI
JO - IJMSI
VL - 17
IS - 1
PY - 2022
Y1 - 2022/4/01
TI - Distributive Lattices of λ-simple Semirings
TT -
N2 - 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.
SP - 47
EP - 55
AU - Mondal, T.
AD - Department of Mathematics Dr. Bhupendra Nath Duta Smriti Mahavidyalaya, Hatgobindapur, Burdwan - 713407, West Bengal, India
KW - Principal left k-radical
KW - Distributive lattice congruence
KW - Completely semiprime k-ideal
KW - λ-simple semiring
KW - Distributive lattice decomposition
UR - http://ijmsi.ir/article-1-1320-en.html
DO - 10.52547/ijmsi.17.1.47
ER -