强π-Rickart模

STRONGLY π-RICKART MODULES

引入了强π-Rickart模的概念.称M为强π-Rickart模,若对任意的f∈End_R(M),存在正整数n,使得r_M(f^n)是M的完全不变直和项.研究了它的一些基本性质,探讨了强π-Rickart模与强Rickart模、π-Rickart模之间的关系,并证明了强π-Rickart模保持直和项.

The concept of strongly π-Rickart modules is introduced. A module M is called strongly π-Rickart if for any f ∈ EndR（M）, there exists a positive integer n such that rM（fn） is a fully invariant direct summand of M. Its basic properties are studied and the relationships among strongly π-Rickart modules, strongly Rickart modules and π-Rickart modules are investigated. In addition, it is proved that any direct summand of a strongly π-Riclat module is also strongly π-Rickart.