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Semirings and their Applications
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In this paper, the authors define Hemirings and semirings as "sets and relations with values with values in a semiring" and define a set of conditions on semimodal construction.Abstract:
Preface. 1. Hemirings and semirings: definitions and examples. 2. Sets and relations with values in a semiring. 3. Building new semirings from old. 4. Some conditions on semirings. 5. Complemented elements in semirings. 6. Ideals in semirings. 7. Prime and semiprime ideals in semirings. 8. Factor semirings. 9. Morphisms of semirings. 10. Kernels of morphisms. 11. Semirings of fractions. 12. Euclidean semirings. 13. Additively-regular semirings. 14. Semimodules over semirings. 15. Factor semimodules. 16. Some constructions for semimodules. 17. Free, projective, and injective semimodules. 18. Localization of semimodules. 19. Linear algebra over a semiring. 20. Partially-ordered semirings. 21. Lattice-ordered semirings. 22. Complete semirings. 23. Complete semimodules. 24. CLO-semirings. 25. Fixed points of affine maps. References. Index of applications. Index of terminology.read more
Citations
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