Commun. Math. Res., 30 (2014), pp. 97-105.
Published online: 2021-05
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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 $S = [Y ; G_α; \phi_{α, β}]$.
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 $S = [Y ; G_α; \phi_{α, β}]$.