abstract
- © 2019 Korean Mathematical Society. For M¿¿ R-Mod, N ¿ M and L ¿ ¿ [M] we consider the product N M L = f ¿Hom (M,L) f(N). A module N ¿ ¿ [M] is called an M-multiplication module R if for every submodule L of N, there exists a submodule I of M such that L = I M N. We extend some important results given for multiplication modules to M-multiplication modules. As applications we obtain some new results when M is a semiprime Goldie module. In particular we prove that M is a semiprime Goldie module with an essential socle and N ¿ ¿ [M] is an M-multiplication module, then N is cyclic, distributive and semisimple module. To prove these results we have had to develop new methods.