Arithmetical Properties of Commutative Rings and Monoids

This book comprises the joint proceedings of the Special AMS session ‘Commutative Rings and Monoids’ and the Mini-Conference ‘Factorization Properties of Commutative Rings and Monoids’ held at the University of Northern Carolina in the autumn of 2003. The volume consists of both original research papers and surveys on arithmetical properties of commutative rings and monoids. The focus is on factorization of elements in a domain or a commutative monoid; however, factorizations of ideals and the non-domain case are also considered. The first seven papers of the volume are based on the main talks of the mini-conference delivered by D. D. Anderson (non-atomic unique factorization), D. F. Anderson (divisibility properties in the graded case), J. Coykendall (extensions of half-factorial domains), F. Halter-Koch and A. Geroldinger (C-monoids, C-domains, transfer principles) and U. Krause (Cale monoids). There are nineteen more papers in the volume, written by other leading experts in the area, including S. Glaz, W. Hassler, E. Houston and B. Olberding. The book is indispensable for anyone interested in current trends, methods and results on the arithmetic of commutative rings.

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