ISSN 2456-0235

​​​​​International Journal of Modern Science and Technology, Vol. 2, No. 5, 2017, Pages 223-227.

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​Sub implicative ideals of KU-Algebras  

S. M. Mostafa, R. A. K Omar, O. W. Abd El- Baseer
Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt.
​​​*Corresponding author’s e-mail: samymostafa@yahoo.com

​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; Kp-ideal.

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International Journal of Modern Science and Technology

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