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arXiv · 1509.02997

Toward Homological Structure Theory of Semimodules: On Semirings All of Whose Cyclic Semimodules Are Projective

S. N. Il'in·Y. Katsov·T. G. Nam
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Abstract

In this paper, we introduce homological structure theory of semirings and CP-semirings---semirings all of whose cyclic semimodules are projective. We completely describe semisimple, Gelfand, subtractive, and anti-bounded, CP-semirings. We give complete characterizations of congruence-simple subtractive and congruence-simple anti-bounded CP-semirings, which solve two earlier open problems for these classes of semirings. We also study in detail the properties of semimodules over Boolean algebras whose endomorphism semirings are CP-semirings; and, as a consequence of this result, we give a complete description of ideal-simple CP-semirings.

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S. N. Il'in, Y. Katsov, T. G. Nam. 2015-09-10. Toward Homological Structure Theory of Semimodules: On Semirings All of Whose Cyclic Semimodules Are Projective. https://arxiv.org/abs/1509.02997

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