关于有序半群的双理想半群

IF 1 Q1 MATHEMATICS Kragujevac Journal of Mathematics Pub Date : 2023-01-01 DOI:10.46793/kgjmat2303.339m

SUSMITA MALLICK, KALYAN HANSDA

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引用次数: 1

摘要

摘要利用S的所有双理想的关联半群B(S)的性质来刻画有序半群S，证明了有序半群S是Clifford有序半群当且仅当B(S)是半格。当且仅当有序半群S同时是正则和正则内半群时，半群B(S)是正规带。对于波段的每个子变种V，我们对有序半群S进行了表征，使得B(S)∈V。

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On the Semigroup of Bi-Ideals of an Ordered Semigroup

The purpose of this paper is to characterize an ordered semigroup S in terms of the properties of the associated semigroup B(S) of all bi-ideals of S. We show that an ordered semigroup S is a Clifford ordered semigroup if and only if B(S) is a semilattice. The semigroup B(S) is a normal band if and only if the ordered semigroup S is both regular and intra regular. For each subvariety V of bands, we characterize the ordered semigroup S such that B(S) ∈ V.

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