摘要
Let R be a commutative ring with identity,M be an R-module,L(M)denote the set of all submodules of M and g■(M)\{OM}.For any submodule N of M,we set gV^(d)(N)={K∈g:K■N}and gζ^(d)(M)=(GV^(d)(N):N■L(M)).Consider χ■L(R)\{R},where L(R)is the set of all ideals of R.We set χV(I)=(J∈x:I■J)and χζ(R)={xV(I):I■L(R)}for any ideal I of R.In this paper,we investigate when,for arbitrary χ and g as above,χζ(R)and gζ^(d)(M)form a topology and a semimodule,respectively.We investigate the structure of gζ^(d)(M)in the case that it is a semimodule.
