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Quasi-Normal Relations - a New Class of Relations

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In this paper, concepts of quasi-normal and dually quasi-normal relations are introduced. Characterizations of these relations are obtained. In addition, particulary we show that the anti-order relation (=≤C) is a (dually) quasi-normal relation if and only if the partially ordered set (X, ) is an anti-chain.

Abstract

In this paper, concepts of quasi-normal and dually quasi-normal relations are introduced. Characterizations of these relations are obtained. In addition, particulary we show that the anti-order relation (=≤C) is a (dually) quasi-normal relation if and only if the partially ordered set (X, ) is an anti-chain.

참고문헌 (11)

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  4. Jiang Guanghao., "Conjugative Relations and Applications", Semigroup Forum, 80(1), pp.85~91 (2010)
  5. Jiang Guanghao., "Dually normal relations on sets", Semigroup Forum, 85(1), pp.75~80 (2012)
  6. Jiang Guanghao., "Normal Relations on Sets and Applications", Int. J. Contemp. Math. Sciences, 6(15), pp.721~726 (2011)
  7. G. Markowsky, "Idempotents and product representations with applications to the semi-group of binary relations", Semigroup Forum, 5, pp.95~119 (1972)
  8. B. M. Schein, "Regular elements of the semigroup of all binary relations", Semigroup Forum, 13, pp.95~102 (1976)
  9. K. A. Zaretskii, "Regular elements of the semigroup of binary relations", Uspehi Matem. Nauk, 3(105), pp.177~179 (1962)
  10. K. A. Zareckii, "The semigroup of binary relations", Mat. Sb, 61, pp.291~305 (1963)
  11. Xu Xiao-quan ., "Domain Theory, Logic, and Computation", pp.65~74 (2003), Kluwer Academic Publisher

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