Weakly regular modules over normal rings |
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Authors: | A N Abyzov |
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Institution: | (1) Chebotarev Research Institute of Mathematics and Mechanics, Kazan, Russia |
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Abstract: | Under study are some conditions for the weakly regular modules to be closed under direct sums and the rings over which all modules are weakly regular. For an arbitrary right R-module M, we prove that every module in the category σ(M) is weakly regular if and only if each module in σ(M) is either semisimple or contains a nonzero M-injective submodule. We describe the normal rings over which all modules are weakly regular. |
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Keywords: | semiartinian ring SV-ring regular ring weakly regular ring |
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