Cubic Q-positive implicative ideals in Q-algebras.

Habib, Hussein Abbas; Kareem, Fatema Faisal

doi:10.24271/psr.2026.572190.2563

Cubic Q-positive implicative ideals in Q-algebras.

Document Type : Original Article

Authors

Hussein Abbas Habib

Fatema faisal Kareem

Department of Mathematics, Ibn-Al-Haitham college of Education, University of Baghdad, Iraq

10.24271/psr.2026.572190.2563

Abstract

A cubic Q-algebra is a generalization of a fuzzy Q-algebra. This work explores important concepts in Q-algebras, including cubic Q-positive implicative ideals, cubic Q-implicative ideals, and cubic Q-commutative ideals, and investigates their fundamental properties. The most important results obtained are: In a commutative Q-algebra. If any ideal is a cubic positive Q-implicative ideal, then it is a cubic Q-implicative ideal. But the converse does not hold. There is no connection between cubic positive Q-implicative ideals and cubic Q-commutative ideals, nor is there a relationship between cubic Q-implicative ideals and cubic Q-commutative ideals. Any cubic Q-positive implicative ideal is a cubic BCK-ideal, and the converse statement is true under certain conditions.

Keywords

Q-algebra

cubic Q-ideal

cubic Q-positive implicative ideals

cubic Q-commutative ideals

a cubic Q-implicative ideal