Strongly primary ideals in rings with zero-divisors

Abstract

Let A be an integral domain with quotient field K. A. Badawi and E. Houston called a strongly primary ideal I of A if whenever x; y ∈ K and xy ∈ I, we have x ∈ I or yn ∈ I for some n ≥ 1. In this note, we study the generalization of strongly primary ideal to the context of arbitrary  commutative rings. We dene a primary ideal P of A to be strongly primary if for each a; b ∈ A, we have aP⊆ bA or bⁿA ⊆ aⁿP for some n ≥ 1.

Key words: Primary, strongly primary, trivial ring extension, amalgamated duplication.