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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 4, Pages 721–738
(Mi smj1873)
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This article is cited in 13 scientific papers (total in 13 papers)
Weakly regular modules over normal rings
A. N. Abyzov N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University
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 $\sigma(M)$ is weakly regular if and only if each module in $\sigma(M)$ is either semisimple or contains a nonzero $M$-injective submodule. We describe the normal rings over which all modules are weakly regular.
Keywords:
semiartinian ring, $SV$-ring, regular ring, weakly regular ring.
Received: 26.01.2007
Citation:
A. N. Abyzov, “Weakly regular modules over normal rings”, Sibirsk. Mat. Zh., 49:4 (2008), 721–738; Siberian Math. J., 49:4 (2008), 575–586
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https://www.mathnet.ru/eng/smj1873 https://www.mathnet.ru/eng/smj/v49/i4/p721
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Abstract page: | 320 | Full-text PDF : | 103 | References: | 49 | First page: | 5 |
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