Ideals that are an irredundant union of principal ideals
This paper investigates the representation of an ideal in a commutative ring as an irredundant of principal ideals. Theorem 1 provides necessary and sufficient condition in order an ideal of a ring \(R\) to be an irredundant union of principal ideals. Moreover, the authors show that each ideal of a ring \(R\) is an irredundant union of principal ideals if and only if \(R\) satisfies the ascending chain condition on principal ideals. Finally, Theorem 3 states that a prime ideal is an irredundant union of principal ideals if and only if it is a union of principal ideals generated by irreducible elements.
scientific article; zbMATH DE number 6113993