JAN OKNINSKI is an Assistant Professor at Warsaw University, Warsaw, Poland. The author or coauthor of several papers in the areas of ring theory, semigroup rings, and semigroups, he is a member of the Polish Mathematical Society and American Mathematical Society. He received the M.Sc. (1977) and Ph.D. (1982) degrees in mathematics from Warsaw University.
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.
Über den Autor
JAN OKNINSKI is an Assistant Professor at Warsaw University, Warsaw, Poland. The author or coauthor of several papers in the areas of ring theory, semigroup rings, and semigroups, he is a member of the Polish Mathematical Society and American Mathematical Society. He received the M.Sc. (1977) and Ph.D. (1982) degrees in mathematics from Warsaw University.
Inhaltsverzeichnis
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.
Klappentext
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
