In this paper we show that the definition and construction of radical and semisimple classes of associative rings can be interpreted in a general category K in terms of two subclasses of epimorphisms and mono-morphisms. We also provide answers to the following two questions posed by Wiegandt: 1. Which objects should be excluded when defining radical and semisimple classes? 2. Given a concrete category, what should the relationship be between the objects used in defining radical and semisimple classes?. AMS(MOS) codes: 18E40, 16A21.
ASJC Scopus subject areas
- Mathematics (miscellaneous)