On weakly δ-rad-semiprimary ideals of commutative rings

In this paper, we introduce and study a new class of ideals termed (weakly) [Formula: see text]-rad-semiprimary. A proper ideal [Formula: see text] of a commutative ring [Formula: see text] is called (weakly) [Formula: see text]-rad-semiprimary provided that whenever [Formula: see text], [Formula: see text] implies either [Formula: see text] or [Formula: see text]. This approach unifies different related classes of ideals. In particular, it generalizes (weakly) [Formula: see text]-semiprimary ideals. Moreover, we investigate the introduced class of ideals within various basic ring constructions such as product rings, quotient rings and trivial ring extensions.