Number systems over orders
نویسندگان
چکیده
منابع مشابه
Waring’s Problem for Matrices over Orders in Algebraic Number Fields
In this paper we give necessary and sufficient trace conditions for an n×n matrix over any commutative and associative ring with unity to be a sum of k-th powers of matrices over that ring, where n, k ≥ 2 are integers. We prove a discriminant criterion for every 2×2 matrix over an order R in an algebraic number field to be a sum of cubes and fourth powers of matrices over R. We also show that i...
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Let F be a field and F[x, y] the ring of polynomials in two variables over F. Let f ∈ F[x, y] and consider the residue class ring R := F[x, y]/fF[x, y]. Our first aim is to study digit representations in R, i.e., we ask for which f each element r ∈ R admits a digit representation of the form d0 + d1x + · · · + d`x with digits di ∈ F[y] satisfying degy di < degy f . These digit systems are motiv...
متن کاملCircle Orders , N - gon Orders and the Crossing Number of Partial Orders
Let F={P1,...,Pm} be a family of sets. A partial order P(F, <) on F is naturally defined by the condition Pi< Pj iff Pi is contained in Pj. When the elements of F are disks (i.e. circles together with their interiors), P(F, <) is called a circle order; if the elements of F are n-polygons, P(F, <) is called an n-gon order. In this paper we study circle orders and n-gon orders. The crossing numbe...
متن کاملCapitulation for Locally Free Class Groups of Orders of Group Algebras over Number Fields
We prove a capitulation result for locally free class groups of orders of group algebras over number fields. This result allows some control over ramification and so as a corollary we obtain an “arithmetically disjoint capitulation result” for the Galois module structure of rings of integers.
متن کاملCapitulation for Locally Free Class Groups of Orders of Abelian Group Algebras over Number Fields
We prove a capitulation result for locally free class groups of orders of abelian group algebras over number fields. As a corollary, we obtain an “abelian arithmetically disjoint capitulation result” for the Galois module structure of rings of integers.
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2018
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-018-1191-x