This problem occurs naturally during the computation of class groups or unit groups and is therefore important for most applications.
Apr 3, 2006 · This problem occurs naturally during the computation of class groups or unit groups and is therefore important for most applications.
Apr 3, 2006 · DEPENDENCY OF UNITS IN NUMBER FIELDS 1509. Theorem 3.1. The units e1,... , e are multiplicative. L(~),.. . , L(el) are R-linearly independent.
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Nov 23, 2015 · For the full field K, which has three inequivalent complex embeddings, two obviously independent units are α−1 and ωα−1. Again, I'm not going to ...
Feb 14, 2010 · If K/Q is a number field which is not Q or a quadratic imaginary field then, by the Dirichlet unit theorem it has a unit of infinite order.
Missing: Dependency | Show results with:Dependency
Jun 14, 2016 · We discuss three algorithms to find small norm elements in number fields. One of these algorithms is a continued fraction-like algorithm ...
It determines the rank of the group of units in the ring OK of algebraic integers of a number field K. The regulator is a positive real number that determines ...
Missing: Dependency | Show results with:Dependency
In Galois theory, we have fields and vector spaces, and the proof is easy. We can just consider 1, s, s2, ททท , and linear dependence kicks in and gives us a ...
Aug 21, 2024 · Units in number fields are crucial for understanding arithmetic structure. They're invertible elements in the ring of integers, ...
Missing: Dependency | Show results with:Dependency
All three of h(a), d(a) and s(a) are independent of the field K in which we happen to work. Further, h(a¹) = h(a), with obvious analogues for d(a) and s(a).