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 - <p style="text-align: justify;">In this paper we study the closed subsemigroups of a Clifford semigroup.
It is shown that <span style="text-align: justify;">$\{\underset{\alpha \in \overline{Y&#39;}}{\cup} G_{\alpha} | Y&#39; \in P(Y)\}$</span>&nbsp;is the set of all closed subsemigroups of
a Clifford semigroup $S = [Y ; G_α; \phi_{α, β}]$, where $\overline{Y&#39;}$ denotes the subsemilattice of $Y$ generated by $Y&#39;$. 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 $S = [Y ; G_α; \phi_{α, β}]$.<br/></p>