Green's Equivalences on Semigroups of Transformations Preserving Order and an Equivalence Relation

摘要

Let T_X be the full transformation semigroup on the set X, T_E(X)={f∈T_X: Ⅴ(a,b)∈ E,(f(a),f(b))∈ E] be the subsemigroup of T_X determined by an equivalence E on X. In this paper the set X under consideration is a totally ordered set with mn points where m≥ 2 and n≥ 3. The equivalence E has m classes each of which contains