International Journal of Modern Science and Technology · ISSN 2456-0235

Research Article · Life Sciences · Volume 2, Issue 5 · May 2017 · Pages 223–227

Sub implicative ideals of KU-Algebras

S. M. Mostafa, R. A. K Omar, O. W. Abd El- Baseer

  • S. M. Mostafa: Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt.
  • R. A. K Omar: Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt.
  • O. W. Abd El- Baseer: Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt.

Abstract

The notions of ku-sub-implicative ideals, ku-sub-commutative ideals and kp-ideals of ku-algebras are introduced. We show that a nonempty subset of a KU-algebra is a ku-sub-implicative ideal if and only if it is both a ku-sub-commutative ideal and a ku-positive implicative ideal. We discuss the relation between kp-ideal and a ku-sub-implicative ideal and a ku-sub-commutative ideal that is, in ku-algebra any kp-ideal is always ku-sub-implicative and ku-sub-commutative ideals, but the converse is not true. We give a characterization of ku-positive implicative ideals of ku-algebras. Moreover some other properties about ku-sub implicative ideals and ku-sub commutative ideals of ku-algebras are given. We give conditions for ideals to be a ku-sub-implicative ideal, ku-sub-commutative ideal and ku-positive implicative ideal. Moreover we show that any ku-sub-implicative ideal, a ku-sub-commutative ideal and kp-ideal are ideals, but the converse is not true. We verify that, in an implicative ku-algebra every ideal is a ku-sub-commutative. In the end, some algorithms for KU-algebra have been constructed.

Keywords

Ku-algebras; Ku-sub implicative ideals; Ku-sub-commutative; Ku-positive implicative; Kpideal

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