Details the diversity of thought in the fields of commutative algebra and multiplicative ideal theory. This book summarizes findings on classes of going-down domains and the going-down property, emphasizing fresh characterizations and applications, as well as generalizations for commutative rings with zero divisors.
Details the diversity of thought in the fields of commutative algebra and multiplicative ideal theory. This book summarizes findings on classes of going-down domains and the going-down property, emphasizing fresh characterizations and applications, as well as generalizations for commutative rings with zero divisors.
DANIEL D. ANDERSON is Professor of Mathematics at the University oflowa, Iowa City. He is the editor of Factorization in Integral Domains and author or coauthor of over 100 journal publications and book chapters, including several in Zero-Dimensional Commutative Rings and Commutative Ring Theory: Proceedings of the II International Conference (all titles, Marcel Dekker, Inc.). A member of the American Mathematical Society and the Mathematical Association of America, Dr. Anderson received the B.A. degree (1971) from the University of Iowa, Iowa City, and the M.S. (1971) and Ph.D. (1974) degrees from the University of Chicago, Illinois. IRA J. PAPICK is Professor of Mathematics at the University of Missouri, Columbia. The author or coauthor of many key professional papers, as well as the book Prufer Domains (Marcel Dekker, Inc.), Dr. Papick is a member of the American Mathematical Society. He received the Ph.D. degree (1975) in mathematics from Rutgers University, New Brunswick, New Jersey.
Inhaltsangabe
Preface Contributors 1. F-Rational Rings and the Integral Closures of Ideals II 2. Cancellation Modules and Related Modules 3. Abstract Ideal Theory from Krull to the Present 4. Conditions Equivalent to Seminormality in Certain Classes of Commutative Rings 5. The Zero-Divisor Graph of a Commutative Ring II 6. Some Examples of Locally Divided Rings 7. On the Dimension of the Jacquet Module of a Certain Induced Representation 8. m-Canonical Ideals in Integral Domains II 9. The t- and v-Spectra of the Ring of Integer-Valued Polynomials Over a Valuation Domain 10. Weakly Factorial Rings with Zero Divisors 11. Equivalence Classes of Minimal Zero-Sequences Modulo a Prime 12. Towards a Criterion for Isomorphisms of Complexes 13. Ideals Having a One-Dimensional Fiber Cone 14. Recent Progress on Going-Down II 15. Kronecker Function Rings: A General Approach 16. On the Complete Integral Closure of the Rees Algebra 17. A New Criterion for Embeddability in a Zero-Dimensional Commutative Ring 18. Finite Conductor Properties of R(X) and R 19. Building Noetherian and Non-Noetherian Integral Domains Using Power Series 20. Integrality Properties in Rings with Zero Divisors 21. Prime-Producing Cubic Polynomials 22. Stability of Ideals and Its Applications 23. Categorically Domains: Highlighting the (Domain) Work of James A. Huckaba Index
Preface Contributors 1. F-Rational Rings and the Integral Closures of Ideals II 2. Cancellation Modules and Related Modules 3. Abstract Ideal Theory from Krull to the Present 4. Conditions Equivalent to Seminormality in Certain Classes of Commutative Rings 5. The Zero-Divisor Graph of a Commutative Ring II 6. Some Examples of Locally Divided Rings 7. On the Dimension of the Jacquet Module of a Certain Induced Representation 8. m-Canonical Ideals in Integral Domains II 9. The t- and v-Spectra of the Ring of Integer-Valued Polynomials Over a Valuation Domain 10. Weakly Factorial Rings with Zero Divisors 11. Equivalence Classes of Minimal Zero-Sequences Modulo a Prime 12. Towards a Criterion for Isomorphisms of Complexes 13. Ideals Having a One-Dimensional Fiber Cone 14. Recent Progress on Going-Down II 15. Kronecker Function Rings: A General Approach 16. On the Complete Integral Closure of the Rees Algebra 17. A New Criterion for Embeddability in a Zero-Dimensional Commutative Ring 18. Finite Conductor Properties of R(X) and R 19. Building Noetherian and Non-Noetherian Integral Domains Using Power Series 20. Integrality Properties in Rings with Zero Divisors 21. Prime-Producing Cubic Polynomials 22. Stability of Ideals and Its Applications 23. Categorically Domains: Highlighting the (Domain) Work of James A. Huckaba Index
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