STRUCTURE OF VIRTUALLY SEMISIMPLE RING - Zulkharnain Purnamaadi, Dedy
Semisimple module is one of modules class that have important role in module theory and its application. One of the most important result in this topic is Wedderburn-Artin Theorem. In this book, we give natural generalization of semisimple modules and generalization of Wedderburn-Artin Theorem. Then, we investigate modules RM that every submodules of M are direct summand of M, then we called that module as virtually semisimple module. We say that module RM is completely virtually semisimple module if every submodules of M are virtually semisimple R-modules. After that, a ring R called (completely) virtually semisimple ring if left R-module R is a (completely) virtually semisimple module. Generalized Wedderburn-Artin Theorem say that R is completely virtually semisimple ring if and only if R = Qk i=1Mni(Di) where Di principal left ideal domain for every i = 1; : : : ; k, and k; n1; : : : ; nk 2 N.