  In this paper, we study the classes of rings in which every proper (regular)
ideal can be factored as an invertible ideal times a nonempty product of proper
radical ideals. More precisely, we investigate the stability of these
properties under homomorphic image and their transfer to various contexts of
constructions such as direct product, trivial ring extension and amalgamated
duplication of a ring along an ideal. Our results generate examples that enrich
the current literature with new and original families of rings satisfying these
properties.
