Semigroup Algebras

Gathers and unifies the results of the theory of noncommutative semigroup rings, primarily drawing on the literature of the last 10 years, and including several new results. Okninski (Warsaw U., Poland) restricts coverage to the ring theoretical properties for which a systematic treatment is current Preface -- Part I. Semigroups and Their Algebras -- 1. Completely 0-Simple and Linear Semigroups -- 2. Semigroups with Finiteness Conditions -- 3. Weakly Periodic Semigroups -- 4. Semigroup Algebras: General Results and Techniques -- 5. Munn Algebras -- 6. Gradations -- Part II. Semigroup Algebras of Cancellative Semigroups -- 7. Groups of Fractions -- 8. Semigroups of Polynomial Growth -- 9. ����-Methods -- 10. Unique- {Two-Unique-Product Semigroups -- 11. Subsemigroups of Polycyclic-by-Finite Groups -- Part III. Finiteness Conditions -- 12. Noetherian Semigroup Algebras -- 13. Spectral Properties -- 14. Descending Chain Conditions -- 15. Regular Algebras -- 16. Self-Injectivity -- 17. Other Finiteness Conditions: A Survey -- Part rv. Semigroup Algebras Satisfying Polynomial Identities -- 18. Preliminaries on PI-Algebras -- 19. Semigroups Satisfying Permutational Property -- 20. PJ-Semigroup Algebras -- 21. The Radical -- 22. Prime PI-Algebras -- 23l Dimensions -- 24l Monomial Algebras -- 25l Azumaya Algebras -- Part V. Problems -- References -- Index.