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This article is cited in 4 scientific papers (total in 4 papers)
Rings over which each module possesses a maximal submodule
A. A. Tuganbaev
Moscow Power Engineering Institute (Technical University)
Abstract:
Right Bass rings are investigated, that is, rings over which any nonzero right module has a maximal submodule. In particular, it is proved that if any prime quotient ring of a ring $A$ is algebraic over its center, then $A$ is a right perfect ring $\iff$ $A$ is a right Bass ring that contains no infinite set of orthogonal idempotents.
DOI:
https://doi.org/10.4213/mzm1514
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English version:
Mathematical Notes, 1997, 61:3, 333–339
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UDC:
512.55
Received: 05.09.1995
Citation:
A. A. Tuganbaev, “Rings over which each module possesses a maximal submodule”, Mat. Zametki, 61:3 (1997), 407–415; Math. Notes, 61:3 (1997), 333–339
Citation in format AMSBIB
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\jour Mat. Zametki
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\vol 61
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\pages 407--415
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\transl
\jour Math. Notes
\yr 1997
\vol 61
\issue 3
\pages 333--339
\crossref{https://doi.org/10.1007/BF02355415}
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http://mi.mathnet.ru/eng/mz1514https://doi.org/10.4213/mzm1514 http://mi.mathnet.ru/eng/mz/v61/i3/p407
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This publication is cited in the following articles:
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Xue, WM, “Two questions on rings whose modules have maximal submodules”, Communications in Algebra, 28:5 (2000), 2633
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Artemovych, OD, “Rigid right bass rings”, Algebra Colloquium, 11:4 (2004), 527
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A. A. Tuganbaev, “Modules with Nakayama's property”, J. Math. Sci., 193:4 (2013), 601–605
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Alhilali H. Ibrahim Ya. Puninski G. Yousif M., “When R Is a Testing Module For Projectivity?”, J. Algebra, 484 (2017), 198–206
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