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A modulus for a number field $K$ is a formal product $$ \prod_{\p} \p^{n_\p} $$ where
A modulus can be written as a product of its finite part $$ \prod_{\p \text{ finite}} \p^{n_\p} $$ and its infinite part $$ \prod_{\p \text{ real}} \p^{n_\p}, $$ with the finite part equal to some ideal in the ring of integers $\mathcal{O}_K$ of $K$ , and the infinite part equal to the product of some subcollection of the real primes of $K$ .
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"modulus" is owned by djao.
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Cross-references: ring of integers, ideal, infinite, finite, complex prime, real prime, integers, exponents, infinite primes, finite primes, product, number field
There are 13 references to this entry.
This is version 1 of modulus, born on 2002-04-16.
Object id is 2841, canonical name is Modulus.
Accessed 5122 times total.
Classification:
| AMS MSC: | 11R37 (Number theory :: Algebraic number theory: global fields :: Class field theory) |
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Pending Errata and Addenda
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