Abstract
A module M over a ring R is said to be purely Rickart if the right annihilator in M of each endomorphism ring of a module M is a pure submodule of M. Purely Rickart module is a proper generalization of Rickart module. Some properties of the purely Rickart module are investigated. Also, we prove that the ring nxn matrix over R is a purely Rickart ring if and only if R is a weakly n-semiherditary ring. Every n-generated projective module is purely Rickart if and only if the free R-module R (n) is a purely Rickart. Others results are provided in this paper.
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