Abstract
The stronglynatural ordered semilattice decomposition of some special class of ordered Clifford semigroups and a subdirect structure of an ordered semigroup which is a stronglynatural ordered semilattice of ordered semigroups without zero elements are given. Relationships between natural ordered semilattice pseudo-orders and proper filters of ordered semigroups are obtained, and the least natural ordered semilattice pseudo-order on an ordered semigroup is constructed.
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