科研之友
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摘要
Let T-X be the full transformation semigroup on a set X and E be a nontrivial equivalence on X. Write
T-E(X) = {f is an element of T-X vertical bar for all (x, y) is an element of E, (f(x), f(y)) is an element of E},
then T-E(X) is a subsemigroup of T-X. In this paper, we endow T-E(X) with the so-called natural order and determine when two elements of T-E(X) are related under this order, then find out elements of T-E(X) which are compatible with <= on T-E(X). Also, the maximal and minimal elements and the covering elements are described.
