A Note On φ- Strongly Quasi Primary Ideals

Our aim in this study is to define the φ-sq primary ideal, which is a prime ideal generalization, and investigate some of its fundamental characteristics. Given a commutative ring R that has an identity, L(R) denotes the set of all ideals of R. Assume that φ : L(R) → L(R) ∪ {∅} a function. A proper ideal I of R is called φ-sq primary ideal if ab ∈ I − φ(I) implies a2 ∈ I or b ∈ √I for each a, b ∈ R. Afterwards, the basic features of this new structure were determined and its relationship with other ideals such as φ-2 prime ideal, strongly quasi primary ideal and φ-semiprimary ideal was examined.