21 Übersetzungen
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Anwendungsbeispiele Englisch
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- The classic reason (due to Serre) is that if "X" is a supersingular elliptic curve, then its endomorphism ring is a maximal order in a quaternion algebra "B" over Q ramified at "p" and ∞.
- In positive characteristic it is possible for the endomorphism ring to be even larger: it can be an order in a quaternion algebra of dimension 4, in which case the elliptic curve is supersingular.
- The collection of versors with quaternion multiplication forms a group, and the set of versors is a 3-sphere in the 4-dimensional quaternion algebra.
- A cyclic algebra, introduced by L. E. Dickson, is a generalization of a quaternion algebra.
- He proceeded to Caius College, Cambridge, there taking up a study of the quaternion algebra.
- Furthermore, just as the quaternion algebra H can be viewed as a union of complex planes, so the hyperbolic quaternion algebra is a union of split-complex number planes sharing the same real line.
- Sometimes a redundant fourth number is added to simplify operations with quaternion algebra.
- For example, in the quaternion algebra H, the splitting above shows that the element "t" + "x" i + "y" j + "z" k has reduced norm "t"2 + "x"2 + "y"2 + "z"2 and reduced trace 2"t".
- For example, applying this to a quaternion algebra ("a", "b") over Q gives the quadratic reciprocity law.
- For example, if [...] , then [...] is the usual quaternion algebra.
- in the quaternion algebra, [...] is then the group of norm 1 elements in [...].
© dict.cc English-German dictionary 2024
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