Factorization in integral domains [based on the proceedings of the conference entitled Factorization in Integral Domains, held Mar. 21, 1996, and of the Special Session in Commutative Ring Theory, held Mar. 22-23, 1996, at the 909th Meeting of the America

The contents in this work are taken from both the University of Iowa's Conference on Factorization in Integral Domains, and the 909th Meeting of the American Mathematical Society's Special Session in Commutative Ring Theory held in Iowa City. The text gathers current work on factorization in integral domains and monoids, and the theory of divisibility, emphasizing possible different lengths of factorization into irreducible elements. Based on the recent proceedings of the University of Iowa's Conference on Factorization in Integral Domains and the 909th Meeting of the American Mathematical Society's Special Session in Commutative Ring Theory held in Iowa City, this outstanding volume gathers, for the first time in a single source, current work on factorization in integral domains and monoids and the theory of divisibility -- emphasizing possible different lengths of factorizations into irreducible elements. Including a diverse range of commutative ring theory topics, such as Prufer domains, one-dimensional Noetherian rings, Henselian pullbacks, intersections of prime ideals, integral and complete integral closures, stable ideals and prime ideals in polynomial rings, and the genus class group, Factorization in Integral Domains surveys elasticity...the catenary and tame degrees...the role of monoid-theoretic techniques involving divisor theory and block monoids ...applications of Krull and block monoids to studies of factorization in integral domains... up-to-date results on integral domains with a finite number of nonassociate atoms, with finitely generated groups of divisibility, and integral domains whose monoids of fractional ideals are finitely generated...and more. Written by leading mathematicians representing institutions in the United States, Europe, and the Middle East, Factorization in Integral Domains is an excellent resource for commutative ring theorists, algebraic number theorists, and graduate students in these disciplines.