On Representable Rings and Modules
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In this paper, we determine the structure of rings that have secondary repre sentation (called representable rings) and give some characterizations of these rings. Also, we characterize Artinian rings in terms of representable rings. Then we introduce com pletely representable modules, modules every non-zero submodule of which have secondary representation, and give some necessary and sufficient conditions for a module to be com pletely representable. Finally, we define strongly representable modules and give some conditions under which representable module is strongly representable.
Abstract
In this paper, we determine the structure of rings that have secondary repre sentation (called representable rings) and give some characterizations of these rings. Also, we characterize Artinian rings in terms of representable rings. Then we introduce com pletely representable modules, modules every non-zero submodule of which have secondary representation, and give some necessary and sufficient conditions for a module to be com pletely representable. Finally, we define strongly representable modules and give some conditions under which representable module is strongly representable.
참고문헌 (27)
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