An Observation on the Natural Partial Order of Transformation Semigroups Restricted by an Equivalence Relation
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Abstract
Let be the full transformation semigroup of a set
. We consider the subsemigroup of
defined by
for an arbitrary equivalence relation
on
. The natural partial order on the largest regular subsemigroup of
is discussed in this paper, and we characterize when two regular elements of
are related under this order. Also, their maximal, minimal and covering elements are described.
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