arXiv subjects

Márton Zubor

Publications and source records attributed to Márton Zubor.

2 recordsLinked to original sources

arXiv2016

Semilattice Indecomposable Finite Semigroups With Large Subsemilattices

In this paper we show that if $Y$ is a subsemilattice of a finite semilattice indecomposable semigroup $S$ then $|Y|\leq 2\left\lfloor \frac{|S|-1}{4}\right\rfloor+1$. We also characterize finite semilattice indecomposable semigroups $S$ which contains a subsemilattice $Y$ with $|S|=4k+1$ and $|Y|=2\left\lfloor \frac{|S|-1}{4}\right\rfloor+1=2k+1$. They are special inverse semigroups. Our investigation is based on our new result proved in this paper which characterize finite semilattice indecomposable semigroups with a zero by only use the properties of its semigroup algebra.

math.GR↗

arXiv2015

A Note on Semigroup Algebras of Permutable Semigroups

Let $S$ be a semigroup and $\mathbb F$ be a field. For an ideal $J$ of the semigroup algebra ${\mathbb F}[S]$ of $S$ over $\mathbb F$, let $\varrho _J$ denote the restriction (to $S$) of the congruence on ${\mathbb F}[S]$ defined by the ideal $J$. A semigroup $S$ is called a permutable semigroup if $α\circ β=β\circ α$ is satisfied for all congruences $α$ and $β$ of $S$. In this paper we show that if $S$ is a semilattice or a rectangular band then $φ_{\{S;{\mathbb F}\}}:\ J\mapsto \varrho _J$ is a homomorphism of the semigroup $(Con ({\mathbb F}[S]);\circ )$ into the relations semigroup $({\cal B}_S; \circ )$ if and only if $S$ is a permutable semigroup.

math.RA↗