Browsing by Subject "16D80"
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Item Open Access Dual π-Rickart modules(Sociedad Colombiana de Matematicas, 2012) Ungor, B.; Kurtulmaz, Y.; Halicioglu, S.; Harmanci, A.Let R be an arbitrary ring with identity and M a right R-module with S = EndR(M). In this paper we introduce dual π-Rickart modules as a generalization of π-regular rings as well as that of dual Rickart modules. The module M is said to be dual π-Rickart if for any f ∈ S, there exist e2 = e ∈ S and a positive integer n such that Im fn = eM. We prove that some results of dual Rickart modules can be extended to dual π-Rickart modules for this general settings. We investigate relations between a dual π-Rickart module and its endomorphism ring.Item Open Access On generalized principally quasi-Baer modules(Birkhaeuser Science, 2013) Ungur, B.; Halicioglu, S.; Kurtulmaz, Y.; Harmanci, A.Let R be an associative ring with identity. A right R–module M is called generalized principally quasi–Baer if for any m ∈ M, rR(m R) is left s– unital as an ideal of R and the ring R is said to be right (left) generalized principally quasi–Baer if R is a generalized principally quasi–Baer right (left) R–module. In this paper, we investigate properties of generalized principally quasi–Baer modules and right (left) generalized principally quasi–Baer rings.Item Open Access Symmetric modules over their endomorphism rings(Lugansk Taras Shevchenko National University, 2015) Ungor, B.; Kurtulmaz, Y.; Halicioglu, S.; Harmanci, A.Let R be an arbitrary ring with identity and M a right R-module with S = EndR(M). In this paper, we study right R-modules M having the property for f, g ∈ EndR(M) and for m ∈ M, the condition fgm = 0 implies gfm = 0. We prove that some results of symmetric rings can be extended to symmetric modules for this general setting. © Journal “Algebra and Discrete Mathematics”.