Toward homological structure theory of semimodules: On semirings all of whose cyclic semimodules are projective
| Autor: | S. N. Il'in, T. G. Nam, Yefim Katsov |
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| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Endomorphism Subtractive color Mathematics::General Mathematics Mathematics::Rings and Algebras 010102 general mathematics Mathematics - Rings and Algebras 010103 numerical & computational mathematics 01 natural sciences Rings and Algebras (math.RA) FOS: Mathematics 0101 mathematics Projective test Computer Science::Formal Languages and Automata Theory Mathematics |
| Zdroj: | Journal of Algebra. 476:238-266 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2016.12.013 |
| Popis: | 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. Comment: 32 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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