Acta Mathematica Hungarica

, Volume 150, Issue 2, pp 512–523 | Cite as

Semilattice indecomposable finite semigroups with large subsemilattices

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Abstract

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 contain 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 characterizes finite semilattice indecomposable semigroups with a zero by using only the properties of its semigroup algebra.

Key words and phrases

semigroup semilattice semigroup algebra 

Mathematics Subject Classification

20M10 
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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2016

Authors and Affiliations

  1. 1.Department of AlgebraBudapest University of Technology and EconomicsBudapestHungary

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