Geodesic
Semirings satisfying the Baer criterion
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2013), pp. 33-39

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It is well-known that for modules over rings the Baer injectivity criterion takes place. In this paper we prove that under one additional condition this criterion is also valid for modules over semirings. We prove that a semiring $S$ satisfies the Baer criterion if and only if all injective (with respect to one-sided ideals of $S$) semimodules satisfy the above condition. We propose a new method for constructing semirings satisfying the Baer criterion.
Keywords: semiring, injective semimodule, Baer criterion. 
@article{IVM_2013_3_a2,
     author = {S. N. Il'in},
     title = {Semirings satisfying the {Baer} criterion},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {33--39},
     publisher = {mathdoc},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_3_a2/}
}
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S. N. Il'in. Semirings satisfying the Baer criterion. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2013), pp. 33-39. http://geodesic.mathdoc.fr/item/IVM_2013_3_a2/