Brendan Goldsmith, Paolo Zanardo
Generalized E-algebras over valuation domains
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.
Forum Mathematicum, Walter de Gruyter
Print ISSN: 0933-7741
Volume: 18, 11/2006
Pages: 1027 - 1040
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