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.
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This work was supported by the National Research, Development and Innovation Office NKFIH, 115288.
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Zubor, M. Semilattice indecomposable finite semigroups with large subsemilattices. Acta Math. Hungar. 150, 512–523 (2016). https://doi.org/10.1007/s10474-016-0657-3
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DOI: https://doi.org/10.1007/s10474-016-0657-3