On (m,n)-closed ideals of commutative rings (original) (raw)

This paper examines (m,n)-closed ideals within the framework of commutative rings, extending the concepts of n-absorbing and semi-n-absorbing ideals. It defines (m,n)-closed ideals, establishes various important properties, and shows that these ideals generalize earlier notions like prime and radical ideals. The study explores implications for radical ideals and their relation to products of proper ideals, presenting a comprehensive view of the significance of (m,n)-closed ideals in ring theory.