منابع مشابه
Projective Modules over Dedekind Domains
In these notes we will first define projective modules and prove some standard properties of those modules. Then we will classify finitely generated projective modules over Dedekind domains Remark 0.1. All rings will be commutative with 1. 1. Projective modules Definition 1.1. Let R be a ring and let M be an R-module. Then M is called projective if for all surjections p : N → N ′ and a map f : ...
متن کاملElliptic Dedekind Domains Revisited
We give an affirmative answer to a 1976 question of M. Rosen: every abelian group is isomorphic to the class group of an elliptic Dedekind domain R. We can choose R to be the integral closure of a PID in a separable quadratic field extension. In particular, this yields new and – we feel – simpler proofs of theorems of L. Claborn and C.R. Leedham-Green. Luther Claborn received his PhD from U. Mi...
متن کاملPrimary Decomposition of Modules over Dedekind Domains Using Gröbner Bases
In [6] was proved that if R is a principal ideal domain and N ⊂ M are submodules of R[x1, . . . , xn], then the primary decomposition for N in M can be computed using Gröbner bases. In this paper we extend this result to Dedekind domains. The procedure that computed the primary decomposition is illustrated with an example.
متن کاملMinimal Prime Ideals of Ore Extensions over Commutative Dedekind Domains
Let R = D[x;σ, δ] be an Ore extension over a commutative Dedekind domain D, where σ is an automorphism on D. In the case δ = 0 Marubayashi et. al. already investigated the class of minimal prime ideals in term of their contraction on the coefficient ring D. In this note we extend this result to a general case δ 6= 0.
متن کاملHermite and Smith normal form algorithms over Dedekind domains
We show how the usual algorithms valid over Euclidean domains, such as the Hermite Normal Form, the modular Hermite Normal Form and the Smith Normal Form can be extended to Dedekind rings. In a sequel to this paper, we will explain the use of these algorithms for computing in relative extensions of number fields. The goal of this paper is to explain how to generalize to a Dedekind domain R many...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2019
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2019.03.016