Cubic Of Positive Implicative Ideals In KU- Semigroup

Fatema. F.  Kareem; Samy M. Mostafa; Omniat.  A. Hasan

doi:10.30526/37.1.3112

Authors

Fatema. F. Kareem Department of Mathematics, College of Education for Pure Sciences, Ibn Al – Haitham, University of Baghdad Iraq
Samy M. Mostafa Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt.
Omniat. A. Hasan Department of Mathematics, College of Education for Pure Sciences Ibn Al – Haitham, University of Baghdad Iraq

DOI:

https://doi.org/10.30526/37.1.3112

Keywords:

A KU-semigroup, cubic ideal, cubic k-ideal, cubic positive implicative ideal, cubic implicative ideal, cubic commutative ideal.

Abstract

In this paper, we define a cubic positive implicative-ideal, a cubic implicative-ideal and a cubic commutative-ideal of a semigroup in KU-algebra as a generalization of a fuzzy (positive implicative-ideal, an implicative-ideal and a commutative-ideal) of a semigroup in KU-algebra. Some relations between these types of cubic ideals are discussed. Also, some important properties of these ideals are studied. Finally, some important theories are discussed. It is proved that every cubic commutative-ideal, cubic positive implicative-ideal, and cubic implicative-ideal are a cubic ideal, but not conversely. Also, we show that if Θ is a cubic positive implicative-ideal and a cubic commutative-ideal then Θ is a cubic implicative-ideal. Some examples of the opposite direction of the previous theories are obtained.

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