N-Rickart Model

In this paper, we mainly study n-Rickart modules, and dual n-Rickart modules.First, we introduce the notion of n-Rickart modules as a special generalizationof Rickart modules. In this section, we study their properties of n-Rickart modules,and provide several characterizations of n-Rickart modules. We also show that everydirect summand of an n-Rickart module is n-Rickart module. In fact, the direct sumof n-Rickart modules which satisfy some conditions is n-Rickart module. Next, weinvestigate the connections between an n-Ricart module and its endomorphism ring,and provide the characterization of n-regular rings in term of n-Rickart modules.Then, we introduce the notion of dual n-Rickart modules. We study theirproperties of n-Rickart modules, and provide several characterizations of dual n-Rickart modules. We also show that the summand of n-Rickart modules inherit theirproperties, and then we show the connections between an dual n-Rickart module andits endomorphism ring.