Abstract
We study the semirings whose simple semimodules are all projective. In particular, we establish that for every semiring S this condition implies the injectivity of all simple S-semimodules and show that, in contrast to the case of rings, the projectivity of all simple semimodules in general is not a left-right symmetric property.
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The author was supported by the subsidy of the Government Task for Kazan (Volga Region) Federal University (Grant 1.2045.2014).
Kazan. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 2, pp. 281–297, March–April, 2017; DOI: 10.17377/smzh.2017.58.204.
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Il’in, S.N. On semirings whose simple semimodules are projective. Sib Math J 58, 215–226 (2017). https://doi.org/10.1134/S0037446617020045
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DOI: https://doi.org/10.1134/S0037446617020045