Metacommutation of Hurwitz primes
© 2014 American Mathematical Society. Conway and Smith introduced the operation of metacommutation for pairs of primes in the ring of Hurwitz integers in the quaternions. We study the permutation induced on the primes of norm p by a prime of norm q under metacommutation, where p and q are distinct r...
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| Format: | Article |
| Language: | English |
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American Mathematical Society (AMS)
2021
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| Online Access: | https://hdl.handle.net/1721.1/133863 |
| Summary: | © 2014 American Mathematical Society. Conway and Smith introduced the operation of metacommutation for pairs of primes in the ring of Hurwitz integers in the quaternions. We study the permutation induced on the primes of norm p by a prime of norm q under metacommutation, where p and q are distinct rational primes. In particular, we show that the sign of this permutation is the quadratic character of q modulo p. |
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