×

zbMATH — the first resource for mathematics

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

MSC:
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
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Berwick, W.E.H., Integral bases, Cambridge tracts in mathematics and mathematical physics, no. 22, (1927), Cambridge
[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
[5] Zassenhaus, H., On the second round or the maximal order program, (), 398-431
[6] Zassenhaus, H., On hensel factorization, II, (), 499-513
[7] Zassenhaus, H., On structural stability, Commun, alg., 8, 1799-1844, (1980) · Zbl 0502.16005
[8] Zassenhaus, H., R. lands verfeinerung des D. Ford’schen ordmax-algorithmus, (1984), Saarbrucken, Manuscript, 1984
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.