On certain semigroups of transformations that preserve double direction equivalence

Document Type : Research Paper

Author

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

Abstract

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).

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Main Subjects


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Volume 42, Issue 4 - Serial Number 4
August 2016
Pages 1015-1024
  • Receive Date: 25 February 2014
  • Revise Date: 03 April 2015
  • Accept Date: 25 May 2015
  • First Publish Date: 01 August 2016