Functional representations of semirings. (English. Russian original) Zbl 1290.16049
J. Math. Sci., New York 187, No. 2, 187-267 (2012); translation from Fundam. Prikl. Mat. 17, No. 3, 111-227 (2012).
In the paper, the author develops the theory of sheaf representations of semirings. The considered classes of semirings are those of symmetric semirings, reduced semirings, Gelfand semirings, regular semirings, Rickart semirings. After presenting the general theory of functional representations of semirings, the author gives the structural representations of semirings and semimodules, more precisely the representations of semimodules by sections of sheaves, representations of Rickart semirings, representations of Abelian-regular positive semirings and applies them to Gelfand semirings and Mulvey duality.
Reviewer: Mirela Ştefănescu (Constanţa)
MSC:
| 16Y60 | Semirings |
| 16S60 | Associative rings of functions, subdirect products, sheaves of rings |
| 54B40 | Presheaves and sheaves in general topology |
| 18F20 | Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) |
Keywords:
Rickart semirings; reduced regular semirings; symmetric semirings; Gelfand semirings; sheaves; sheaf representations of semirings; representations of semimodulesReferences:
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