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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.
List of contents
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
About the author
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.
Summary
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.
