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The construction of maximal orders over a Dedekind domain. (English) Zbl 0632.13003
Let R be a complete local Dedekind domain with quotient field F, and let f(x) be a monic polynomial in R[x] having non-zero discriminant. The author gives a new algorithm for constructing the maximal order of the algebra \(A_ f=F[x]/f(x)F[x]\).
Reviewer: A.Grams

13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
13F20 Polynomial rings and ideals; rings of integer-valued polynomials
13-04 Software, source code, etc. for problems pertaining to commutative algebra
Full Text: DOI
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[2] Ford, D.J., On the computation of the maximal order in a Dedekind domain, Ph.D. dissertation, (1978), Ohio State University
[3] Weiss, E., Algebraic number theory, (1963), McGraw-Hill New York
[4] Zassenhaus, H., Ein algorithmus zur berechnung einer minimalbasis über gegebener ordnung, (), 90-103 · Zbl 0153.36702
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[8] Zassenhaus, H., R. lands verfeinerung des D. Ford’schen ordmax-algorithmus, (1984), Saarbrucken, Manuscript, 1984
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