On two conjectures concerning-weakly prime ideals in commutative rings

摘要

Let R be a commutative ring with unity. A proper ideal P of R is called (n - 1, n)-weakly prime (n >= 2) if 0 not equal x(1) ... x(n) is an element of P implies x(1) ... x(i-1)x(i+1) ... x(n) is an element of P for some i is an element of {1, ... n}, where x(1), ... , x(n) is an element of R: In 2014, Ebrahimpour [On generalizations of prime ideals (II). Comm. Algebra 42:3861-3875] posed two conjectures on (n - 1, n)-weakly prime ideals. In this paper, we prove them.