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

purpose: to report a case who had optic disc duplication, a rare congenital disorder characterized by two well-defined discs in one eye. case report: a 19 months-old child presented with unilateral epiphora in the right eye since birthday. the right eye was smaller than the left eye and mild ptosis was apparent. nasolacrimal duct probing was performed under general anesthesia. the examination r...

Some completely positive maps on reduced amalgamated free products of C∗–algebras are constructed, showing that every reduced amalgamated free product of exact C∗–algebras is exact. Consequently, every amalgamated free product of exact discrete groups is exact.