ON THE SEMIGROUP OF DIFUNCTIONAL BINARY RELATIONS
In this paper, we have examine some properties of elements of the semigroup , where DX, is the set of all binary relations Î± âŠ† X Ã— X satisfying , (), and is a binary operation on DX defined by () , with xÎ± denoting set of images of x under Î±, and yÎ²âˆ’1 denoting set of pre-images of y under Î². 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.
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 â€“ 234.
Kudryavtseva, G. and Maltcev, V. (2011): Two generalizations of the symmetric inverse semigroup.
Publicationes Mathematicae Debrecen 78, 253 â€“ 282.
Riguet, J. (1948): Relations binaire, fermetures, correspondances de galois. Bulletin Society Mathematics France. 76, 114 â€“ 155.
Vernitski, A. (2007): A generalization of symmetric inverse semigroups. Semigroup Forum 75, 417 â€“ 426.
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