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'fundamental units'
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| Title of object: |
fundamental units |
| Canonical Name: |
FundamentalUnits |
| Type: |
Definition |
| Created on: |
2004-08-06 12:32:22 |
| Modified on: |
2004-08-07 01:47:19 |
| Classification: |
msc:11R04, msc:11R27 |
| Keywords: |
Dirichlet's unit theorem |
Preamble:
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\usepackage{amssymb}
\usepackage{amsmath}
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%\usepackage{psfrag}
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Content:
The ring $R$ of algebraic integers of any algebraic number field contains a finite set $\{\eta_1, \eta_2, ..., \eta_t\}$ of so-called {\em fundamental units} such that every unit $\epsilon$ of $R$ is a power product of them, multiplied by a root of unity:
$$\epsilon = \zeta\cdot\eta_1^{k_1}\eta_2^{k_2}...\eta_t^{k_t}$$
Example: \,units of quadratic fields |
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