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Modules having Baer summands

Calci, T. P.; Halicioglu, S.; Harmanci, A.


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        "affiliation": "Ankara Univ, Dept Math, TR-06100 Ankara, Turkey", 
        "name": "Calci, T. P."
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        "affiliation": "Ankara Univ, Dept Math, TR-06100 Ankara, Turkey", 
        "name": "Halicioglu, S."
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        "affiliation": "Hacettepe Univ, Dept Math, Ankara, Turkey", 
        "name": "Harmanci, A."
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    "description": "Let R be an arbitrary ring with identity and M a right R-module with S= End(R)(M). Let F be a fully invariant submodule of M and I-1(F) denotes the set {m is an element of M : Im subset of F} for any subset I of S. The module M is called F-Baer if I-1(F) is a direct summand of M for every left ideal I of S. This work is devoted to the investigation of properties of F-Baer modules. We use F-Baer modules to decompose a module into two parts consists of a Baer module and a module determined by fully invariant submodule F, namely, for a module M, we show that M is F-Baer if and only if M = F circle plus N where N is a Baer module. By using F-Baer modules, we obtain some new results for Baer rings.", 
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