τ-π-Rickart模

τ-π-Rickart modules

引入了τ-π-Rickart模的概念,其中τ=(T,F)表示遗传挠理论.称M是τ-π-Rickart模,如果对任意g∈End(M),存在正整数n,使得r M(g n)是M的直和因子.研究了τ-π-Rickart模的性质,讨论了τ-π-Rickart模与τ-Rickart模以及π-Rickart模之间的关系,给出了τ-π-Rickart模的子模仍是τ-π-Rickart模的条件,证明了τ-π-Rickart模关于直和因子是封闭的.最后,证明了某些Abelτ-π-Rickart模的类关于有限直和是封闭的.

The concept ofτ-π-Rickart module is introduced,whereτ=(T,F)denotes a hereditary torsion theory.A module M is calledτ-π-Rickart if for any g∈End(M),there exists a positive integer n such that r M(g n)is a direct summand of M.Properties ofτ-π-Rickart module and the relationship amongτ-π-Rickart modules,τ-Rickart modues as well asπ-Rickart modules are investigated,the conditions that submodule ofτ-π-Rickart module isτ-π-Rickart are given,it is proved that any direct summand ofτ-π-Rickart module is alsoτ-π-Rickart.Finally,it is shown that the class of some Abelianτ-π-Rickart modules is closed under finitely direct sums.