JP Journal of Algebra, Number Theory and Applications
Volume 33, Issue 1, Pages 65 - 73
(May 2014)
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FACTORIZATION AND LOCALIZATION
Bronislaw Wajnryb and Abraham Zaks
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Abstract: One of the classical results of Auslander and Buchsbaum concerning local rings states that a regular local ring is a factorial domain (FD). Factorization in a Krull domain R can be stated in terms of the class group namely iff R is an FD. If R is a Dedekind domain and R is an FD, then every overring of R in the field of quotients K of R is a localization of R. An integral domain R is half-factorial (HFD) if every non-invertible element is a finite product of irreducible elements and the number of factors depends only on x. A Krull domain R whose class group is isomorphic to is an HFD. We intend to point out possible generalizations to commutative and non-commutative rings of the various factorizations properties, and to analyze the overrings that are localizations in terms of the properties of their ideals. |
Keywords and phrases: Krull domains, localization, flat overrings. |
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