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A GENERALIZATION OF MULTIPLICATION MODULES

  • Perez, Jaime Castro (Escuela de Ingenieria y Ciencias Instituto Tecnologico y de Estudios Superiores de Monterrey) ;
  • Montes, Jose Rios (Instituto de Matematicas Universidad Nacional Autonoma de Mexico) ;
  • Sanchez, Gustavo Tapia (Instituto de Ingenieria y Tecnologia Universidad Autonoma de Ciudad Juarez)
  • Received : 2018.02.08
  • Accepted : 2018.09.07
  • Published : 2019.01.31

Abstract

For $M{\in}R-Mod$, $N{\subseteq}M$ and $L{\in}{\sigma}[M]$ we consider the product $N_ML={\sum}_{f{\in}Hom_R(M,L)}\;f(N)$. A module $N{\in}{\sigma}[M]$ is called an M-multiplication module if for every submodule L of N, there exists a submodule I of M such that $L=I_MN$. 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 $N{\in}{\sigma}[M]$ is an M-multiplication module, then N is cyclic, distributive and semisimple module. To prove these results we have had to develop new methods.

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