More on the strongly 1-absorbing primary ideals of commutative rings

Let R be a commutative ring with identity. We study the concept of strongly 1-absorbing primary ideals which is a generalization of n-ideals and a subclass of 1-absorbing primary ideals. A proper ideal I of R is called strongly 1-absorbing primary if for all nonunit elements a,b,c ∈ R such that abc ∈ I, it is either ab ∈ I or \(c \in \sqrt 0 \) $$c\in \sqrt{0}$$ . Some properties of strongly 1-absorbing primary ideals are studied. Finally, rings R over which every semi-primary ideal is strongly 1-absorbing primary, and rings R over which every strongly 1-absorbing primary ideal is prime (or primary) are characterized. Many examples are given to illustrate the obtained results.