منابع مشابه
Generalized Factorials and Fixed Divisors over Subsets of a Dedekind Domain
Given a subset X of a Dedekind domain D, and a polynomial F # D[x], the fixed divisor d(X, F ) of F over X is defined to be the ideal in D generated by the elements F(a), a # X. In this paper we derive a simple expression for d(X, F ) explicitly in terms of the coefficients of F, using a generalized notion of ``factorial'' introduced by the author in a previous paper. When X=D=Z, this generaliz...
متن کاملThe Construction of Maximal Orders Over a Dedekind Domain
Suppose R is a complete local Dedekind domain with quotient field F, and let f(x) be a monic polynomial in R[x] having non-zero discriminant. We present here a new algorithm to construct the maximal order of the algebra Af = F[x]/f(x)F[x]. The new algorithm incorporates ideas of Zassenhaus (1975, 1980) concerning P-adic stability and the algebraic decomposition of A s . We show that it is alway...
متن کاملDeterministic polynomial-time test for prime ideals in a Dedekind domain with finite rank
We describe a deterministic polynomial-time test that determining whether a nonzero ideal is a prime ideal in a Dedekind domain with finite rank. The techniques which we used are basis representation of finite rings and the Hermite and Smith normal forms.
متن کاملϕ-ALMOST DEDEKIND RINGS AND $\Phi$-ALMOST DEDEKIND MODULES
The purpose of this paper is to introduce some new classes of rings and modules that are closely related to the classes of almost Dedekind domains and almost Dedekind modules. We introduce the concepts of $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and study some properties of this classes. In this paper we get some equivalent conditions for $\phi$-almost Dedekind rings and ...
متن کاملStable Tameness of Two-Dimensional Polynomial Automorphisms Over a Dedekind Domain
In this paper it is established that all two-dimensional polynomial automorphisms over a Dedekind Q-algebra are stably tame; in fact, they become tame with the addition of three more dimensions. A key element in the proof is this additional new theorem: Over an Artinian Q-algebra all two-dimensional polynomial automorphisms having Jacobian determinant one are tame.
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1998
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-85-3-229-233