ON JOINTLY PRIME RADICALS OF (R,S)-MODULES - Dian Ariesta Yuwaningsih; Indah Emilia Wijayanti (IndoMS, 2015)
Let M be an (R,S)-module. In this paper a generalization of the m-system set of modules to (R,S)-modules is given. Then for an (R,S)-submodule N of M, we define [(R,S)]N as the set of aM such that every m-system containing a meets N. It is shown that [(R,S)]N is the intersection of all jointly prime (R,S)-submodules of M containing N. We define jointly prime radicals of an (R,S)-module M as rad_(R,S)(M)=[(R,S)]0. Then we present some properties of jointly prime radicals of an (R,S)-module.DOI : http://dx.doi.org/10.22342/jims.21.1.199.25-34