Table of Contents

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.