35 research outputs found

    ESSENTIAL EXTENSIONS WITH THE C-EXTENDING PROPERTY

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    Let C be a nonempty subset of the set of submodules of a module M. Then M is called a C-extending module if for each X in ce there exists a direct summand D of M such that X is essential in D. In general, it is known that an essential extension of a C-extending module is not C-extending. In this paper, our goal is to show how to construct essential extensions of a module which are C extending by using a set of representatives of a certain equivalence relation on the set of all idempotent endomorphisms of the injective hull of the module. Also we characterize when the rational hull of a module is C-extending in terms of such a set of representatives. Moreover we show that several well known types of C-extending conditions (e.g., extending and FI-extending) transfer from module to its rational hull

    A note on weak regularity in general rings

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    Principally Goldie*-Lifting Modules

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