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V-semirings

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Abstract

We investigate the semirings over which all simple semimodules are injective. In ring and module theory, the rings with an analogous condition are called V-rings. Therefore it is natural to call the semirings under consideration V-semirings. We obtain the semiring analogs of some well-known results on V-rings, including an analog of Kaplansky’s theorem on commutative V-rings.

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Authors and Affiliations

  1. Lobachevskiĭ Institute of Mathematics and Mechanics, Kazan Federal University, Kazan, Russia

    S. N. Il’in

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  1. S. N. Il’in
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Correspondence to S. N. Il’in.

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Original Russian Text Copyright © 2012 Il’ in S. N.

The author was supported by the Russian Foundation for Basic Research (Grant 10-01-00431-a).

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Translated from Sibirskiı Matematicheskiı Zhurnal, Vol. 53, No. 2, pp. 277–290, March–April, 2012.

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Il’in, S.N. V-semirings. Sib Math J 53, 222–231 (2012). https://doi.org/10.1134/S003744661202005X

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  • DOI: https://doi.org/10.1134/S003744661202005X

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