Browsing by Subject "16U80"

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    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.
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    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.