On certain semigroups of transformations that preserve double direction equivalence

Document Type : Research Paper


School of Mathematical Science‎, ‎Guizhou Normal University‎, ‎Guiyang 550001‎, ‎China.


Let TX be the full transformation semigroups on the set X. For an equivalence E on X, let TE*(X) = {α ∈ TX : ∀(x, y) ∈ E ⇔ (xα, yα) ∈ E} It is known that TE*(X) is a subsemigroup of TX. In this paper, we discuss the Green's *-relations, certain *-ideal and certain Rees quotient semigroup for TE*(X).


Main Subjects

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