On Closed Rickart Modules | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 57, Issue 4, October 2016, Pages 2746-2753 | ||
| Authors | ||
| Inaam Mohammed Ali; ; ar Younis Ghawi | ||
| Abstract | ||
| In this article, we study the notion of closed Rickart modules. A right R-module M is said to be closed Rickart if, for each φ∈End(M), r_M (φ)=Kerφ is a closed submodule of M. Closed Rickart modules is a proper generalization of Rickart modules. Many properties of closed Rickart modules are investigated. Also, we provide some characterizations of closed Rickart modules. A necessary and sufficient condition is provided to ensure that this property is preserved under direct sums. Several connections between closed Rickart modules and other classes of modules are given. It is shown that every closed Rickart module is κ-nonsingular module. Examples which delineate this concept and some results are provided. | ||
| Keywords | ||
| Rickart Modules; Quasi; Dedekind Modules; Closed Simple Modules; Nonsingular Modules | ||
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