In this paper we show that if $Y$ is a subsemilattice of a finite semilatticeindecomposable semigroup $S$ then $|Y|\leq 2\left\lfloor\frac{|S|-1}{4}\right\rfloor+1$. We also characterize finite semilatticeindecomposable semigroups $S$ which contains a subsemilattice $Y$ with$|S|=4k+1$ and $|Y|=2\left\lfloor \frac{|S|-1}{4}\right\rfloor+1=2k+1$. Theyare special inverse semigroups. Our investigation is based on our new resultproved in this paper which characterize finite semilattice indecomposablesemigroups with a zero by only use the properties of its semigroup algebra.
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机译：在本文中，我们证明如果$ Y $是可分解半群$ S $的有限半格的子半子集，则$ | Y | \ leq 2 \ left \ lfloor \ frac {| S | -1} {4} \ right \ rfloor + 1 $。我们还对有限的半格不可分解半群$ S $进行了刻画，其中包含一个具有$ | S | = 4k + 1 $和$ | Y | = 2 \ left \ lfloor \ frac {| S | -1} {4} \正确\ rfloor + 1 = 2k + 1 $。它们是特殊的逆半群。我们的研究基于本文提出的新结果，该结果仅通过使用半群代数的性质来刻画具有零的有限半格不可分解半群。
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