| Abstract: | We show that if Y is a subsemilattice of a finite semilattice indecomposable semigroup S then ({|Y|leq 2leftlfloor frac{|S|-1}{4}rightrfloor+1}). We also characterize finite semilattice indecomposable semigroups S which contain a subsemilattice Y with ({|S|=4k+1}) and ({|Y|=2leftlfloor frac{|S|-1}{4} rightrfloor+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. |
