multiplicative congruence
Let be any real prime of a number field , and write for the corresponding real embedding of . We say two elements are multiplicatively congruent mod if the real numbers and are either both positive or both negative.
Now let be a finite prime of , and write for the localization of the ring of integers of at . For any natural number , we say and are multiplicatively congruent mod if they are members of the same coset of the subgroup of the multiplicative group of .
If is any modulus for , with factorization
then we say and are multiplicatively congruent mod if they are multiplicatively congruent mod for every prime appearing in the factorization of .
Multiplicative congruence of and mod is commonly denoted using the notation
Title | multiplicative congruence |
---|---|
Canonical name | MultiplicativeCongruence |
Date of creation | 2013-03-22 12:50:16 |
Last modified on | 2013-03-22 12:50:16 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 4 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 11R37 |
Synonym | multiplicatively congruent |
Related topic | Congruence2 |