ON SOC - SUPPLEMENTED MODULES

Abstract

Let  A, B  be submodules of module   M . Submodule  A   is said to be a   supplement of  B in  M  nếu  M=A+B  and   Module  M  is called supplemented  if for each submodule A of M, there exists a submodule B of  M such that A is supplement  of B in M.  These classes are studied in recently years. In particular,   some characterizations of perfect and semiperfect ring via supplemented modules.  In 2004, Wang and  Ding  gave a  generalization of supplemented module and research them.  Following which, a module M  is called generalized supplemented  if for each submodule A of M,  there exists a submodule B of M such that  M=A+B  and  In this paper, we consider a generalization of  supplemented module, that is soc-supplemented modules and some applications in classes well-known rings.