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Let  and M be a finitely generated  S-module. We say that M is a Stanley Cohen-Macaulay module if   where  Let  be a simplicial complex on the vertex set  with  Let F be an arbitrary face of  and  be a new vertex. A cone from  over F, denoted by  is the simplex on the vertex set  Set  and  It is shown that if  is a Stanley Cohen-Macaulay module then Stanley’s conjecture holds for  Moreover, we show that for a monomial ideal I of S if  is a regular element on  for some  then I is a Stanley Cohen-Macaulay ideal if and only if  is a Stanley Cohen-Macaulay ideal. 

Stanley depth, Stanley Cohen-Macaulay, prime filtration.