ON THE SEMIGROUP OF DIFUNCTIONAL BINARY 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.
References
East, J. and Vernitski, A. (2018): Ranks of ideals in inverse semigroups of difunctional binary relations. Semigroup Forum. 96, 21 – 30.
Jaoua, A., Elloumi, S., Hasnah, A., Jaam, J. and Nafkha, I. (2004): Discovering regularities in databases using canonical decomposition of binary relations. Journal on Relational methods in Computer Science. 1, 217 – 234.
Kudryavtseva, G. and Maltcev, V. (2011): Two generalizations of the symmetric inverse semigroup.
Publicationes Mathematicae Debrecen 78, 253 – 282.
Riguet, J. (1948): Relations binaire, fermetures, correspondances de galois. Bulletin Society Mathematics France. 76, 114 – 155.
Vernitski, A. (2007): A generalization of symmetric inverse semigroups. Semigroup Forum 75, 417 – 426.
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