相关于稳定挠理论的extending模

Extending Modules Relative to Stable Torsion Theory

设τS表示稳定挠理论.给出了τS-本质子模的等价刻画,讨论了τS-闭子模和闭子模之间的关系,证明了K在M中是τS-闭的当且仅当K是M的包含τS(M)的闭子模,研究了τSextending模的若干性质.进而,给出了τS-extending模的等价刻画,证明了M是τS-extending模当且仅当M=τS(M)⊕M′,其中M′是(τS-挠自由)extending模.

LetτS be a stable torsion theory,some equivalent characterizations ofτS-essential submodule are given,the relations betweenτS-closed submodules and closed submodules are discussed,it is proved that K isτS-closed in M if and only if K containsτS(M)and K is a closed submodule of M,some properties ofτS-extending module are studied.Moreover,some equivalent characterizations ofτS-extending module are given,it is proved that M isτS-extending module if and only if M=τS(M)⊕M′where M′is a(τS-torsion free)extending module.