ON THE SEMIGROUP OF DIFUNCTIONAL BINARY RELATIONS

  • Muhammad Jamilu Ibrahim Department of Mathematics, Sule Lamido University Kafin Hausa Jigawa State Nigeria
  • Ibrahim Mamman Sawudi Department of Mathematics, Federal College of Education, Katsina
  • Abdussamad Tanko Imam Department of Mathematics, Ahmadu Bello University, Zaria
Keywords: Binary relations, Cardinalities, Difunctional relations, Green’s relations

Abstract

In this paper, we have examine some properties of elements of the semigroup , where DX, is the set of all binary relations α ⊆ X × X satisfying , (), and is a binary operation on DX defined by () , with xα denoting set of images of x under α, and yβ−1 denoting set of pre-images of y under β. In particular, we showed that in the semigroup  there is no distinction between the concepts of reflexive and symmetric relations. We also presented a characterization of idempotent elements in  in term of equivalence relations.

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Published
2022-08-15
How to Cite
IbrahimM. J., Sawudi I. M., & ImamA. T. (2022). ON THE SEMIGROUP OF DIFUNCTIONAL BINARY RELATIONS. FUDMA JOURNAL OF SCIENCES, 6(4), 17 - 19. https://doi.org/10.33003/fjs-2022-0604-1026