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Generalized E-algebras over valuation domains
-
Brendan Goldsmith
and
Paolo Zanardo
Published/Copyright:
February 27, 2007
Abstract
Let R be a valuation domain. We investigate the notions of E(R)-algebra and generalized E(R)-algebra and show that for wide classes of maximal valuation domains R, all generalized E(R)-algebras have rank one. As a by-product we prove if R is a maximal valuation domain of finite Krull dimension, then the two notions coincide. We give some examples of E(R)-algebras of finite rank that are decomposable, but show that over Nagata domains of small degree, the E(R)-algebras are, with one exception, the indecomposable finite rank algebras.
Received: 2005-11-08
Accepted: 2005-11-24
Published Online: 2007-02-27
Published in Print: 2006-11-20
© Walter de Gruyter
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Articles in the same Issue
- A summation formula for divisor functions associated to lattices
- On a relative Alexandrov-Fenchel inequality for convex bodies in Euclidean spaces
- Cohomology of harmonic forms on Riemannian manifolds with boundary
- On the structure and characters of weight modules
- On the vanishing of Ext over formal triangular matrix rings
- Homotopy localization of groupoids
- A group-theoretic characterization of the direct product of a ball and a Euclidean space
- Degree-regular triangulations of the double-torus
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