TY - JOUR T1 - The Closed Subsemigroups of a Clifford Semigroup AU - Fu , Yinyin AU - Zhao , Xianzhong JO - Communications in Mathematical Research VL - 2 SP - 97 EP - 105 PY - 2021 DA - 2021/05 SN - 30 DO - http://doi.org/10.13447/j.1674-5647.2014.02.01 UR - https://global-sci.org/intro/article_detail/cmr/18973.html KW - semilattice, closed subsemigroup, Clifford semigroup. AB -

In this paper we study the closed subsemigroups of a Clifford semigroup. It is shown that $\{\underset{\alpha \in \overline{Y'}}{\cup} G_{\alpha} | Y' \in P(Y)\}$ is the set of all closed subsemigroups of a Clifford semigroup $S = [Y ; G_α; \phi_{α, β}]$, where $\overline{Y'}$ denotes the subsemilattice of $Y$ generated by $Y'$. In particular, $G$ is the only closed subsemigroup of itself for a group $G$ and each one of subsemilattices of a semilattice is closed. Also, it is shown that the semiring $\overline{P}(S)$ is isomorphic to the semiring $\overline{P}(Y)$ for a Clifford semigroup $S = [Y ; G_α; \phi_{α, β}]$.