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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

##### 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
##### Keywords:
Dedekind domain; polynomial; maximal order
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##### 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
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