This volume compiles research papers presented at the University of Missouri, Columbia conference. It includes current research that illustrates the diversity of thought in the field of commutative algebra, particularly multiplicative ideal theory. It also presents survey articles on abstract ideal theory, going down, stable domains, prime producing polynomials, and integrality properties in rings with zero divisors. Written by mathematicians representing institutions in the United States, Europe, Asia, and the Middle East, the papers investigate F-rational rings, ideals having one-dimensional fiber cones, and isomorphism of complexes. They also describe seminormality, cancellation modules, and m-canonical ideals. Annotation c. Book News, Inc., Portland, OR (booknews.com)
Includes current work of 38 renowned contributors that details the diversity of thought in the fields of commutative algebra and multiplicative ideal theory. Summarizes recent findings on classes of going-down domains and the going-down property, emphasizing new characterizations and applications, as well as generalizations for commutative rings with zero divisors.
Preface iii Contributors vii F-Rational Rings and the Integral Closures of Ideals II 1(12) Ian M. Aberbach Craig Huneke Cancellation Modules and Related Modules 13(14) D. D. Anderson Abstract Ideal Theory from Krull to the Present 27(22) D. D. Anderson E. W. Johnson Conditions Equivalent to Seminormality in Certain Classes of Commutative Rings 49(12) David F. Anderson Ayman Badawi The Zero-Divisor Graph of a Commutative Ring, II 61(12) David F. Anderson Andera Frazier Aaron Lauve Philip S. Livingston Some Examples of Locally Divided Rings 73(12) Ayman Badawi David E. Dobbs On the Dimension of the Jacquet Module of a Certain Induced Representation 85(4) William Banks Daniel Bump Daniel Lieman m-Canonical Ideals in Integral Domains II 89(20) Valentina Barucci Evan Houston Thomas G. Lucas Ira J. Papick The T-and v-Spectra of the Ring of Integer-Valued Polynomials Over a Valuation Domain 109(10) Paul-Jean Cahen Evan Houston Francesca Tartarone Weakly Factorial Rings with Zero Divisors 119(14) Gyu Whan Chang Equivalence Classes of Minimal Zero-Sequences Modulo a Prime 133(14) Scott T. Chapman Michael Freeze William W. Smith Towards a Criterion for Isomorphisms of Complexes 147(8) S. Dale Cutkosky Hema Srinivasan Ideals Having a One-Dimensional Fiber Cone 155(16) Marco D Anna Anna Guerrieri William Heinzer Recent Progress on Going-Down II 171(18) David E. Dobbs Kronecker Function Rings: A General Approach 189(18) Marco Fontana K. Alan Loper On the Complete Integral Closure of the Rees Algebra 207(16) Stefania Gabelli Anna Guerrieri A New Criterion for Embeddability in a Zero-Dimensional Commutative Ring 223(8) Robert Gilmer Finite Conductor Properties of R(X) and R>X< 231(20) Sarah Glaz Building Noetherian and Non-Noetherian Integral Domains Using Power Series 251(14) William Heinzer Christel Rotthaus Sylvia Wiegand Integrality Properties in Rings with Zero Divisors 265(16) Thomas G. Lucas Prime-Producing Cubic Polynomials 281(38) Joe L. Mott Kermit Rose Stability of Ideals and Its Applications 319(24) Bruce Olberding Categorically Domains: Highlighting the (Domain) Work of James A. Huckaba 343(14) Ira J. Papick Index 357
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.
