(untitled) (Communications in Mathematical Research, 2021)
In this paper we study the closed subsemigroups of a Clifford semigroup. It is shown that {α Y' G_α | Y' P(Y)} is the set of all closed subsemigroups of a Clifford semigroup S = [Y ; G_α; φ_α, β], where 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 P(S) is isomorphic to the semiring P(Y) for a Clifford semigroup S = [Y ; G_α; φ_α, β].