t-Rickart模的性质研究

Property Study of t-Rickart Modules

给出t-Rickart模的概念,称模M R是t-Rickart模,如果S中的任意元素在M中的t-零化子是M的直和项,其中S是它的自同态环。给出t-Rickart模的一些刻画,并研究这类模的基本性质,证明了t-Rickart模的每个直和项仍是t-Rickart模。

The notion of t-Rickart modules is introduced. A module M is called a t-Rickart module, if the t-annihilator in M of any single element of S is generated by an idempotent of S, the S is its endomorphism ring. Some characterizations of t-Rickart modules are given and the basic properties of this kind of modules are studied. It is shown that every direct sum- mand of a t-Rickart module inherits the properties.