2022/01/26 by Тарас Банах, Taras Banakh, Banakh, Taras +2
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Fuzzy and Soft Set Theory #math.GR #math.RA #msc:20M10 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2201.10786
9 pages (this is the first part of the previous paper, which has been split into two parts)
arxiv created 2022/02/13 · arxiv updated 2022/02/15
Given two elements x,y of a semigroup X we write x\lesssim y if for every homomorphism χ:X→\0,1\ we have χ(x)≤χ(y). The quasiorder \lesssim is called the binary quasiorder on X. It induces the equivalence relation \Updownarrow that coincides with the least semilattice congruence on X. In the paper we discuss some known and new properties of the binary quasiorder on semigroups.