division algebra वाक्य
उदाहरण वाक्य
मोबाइल
- Let be any of the four division algebras,,,, and let be the tautological line bundle over the projective line, and its class in K-theory.
- In this section, we consider projective spaces over a commutative field " K ", although most results may be generalized to projective spaces over a division algebra.
- "' Frobenius theorem "': The only finite-dimensional associative division algebras over the reals are the reals themselves, the complex numbers, and the quaternions.
- By the Cayley Hamilton theorem, 0 } } and because is a division algebra, it follows that either 0 } } for some or that 0 } } for some.
- A " finite-dimensional " unital associative algebra ( over any field ) is a division algebra " if and only if " it has no zero divisors.
- For example, Desargues'theorem corresponds to the coordinate ring being obtained from a division ring, while Alternative, not necessarily associative, division algebras like the octonions correspond to Moufang planes.
- The other is that the concept is an analogue to the octonion algebras, and quadratic Jordan division algebras of degree 3, that give rise to Moufang 3-gons and 6-gons.
- The same argument eliminates the possibility of the coefficient field being the reals or the " p "-adic numbers, because the quaternion algebra is still a division algebra over these fields.
- He realized that the Cayley Dickson construction, used to generate division algebras, could be modified ( with a factor gamma ( & gamma; ) ) to construct other composition algebras including the split-octonions.
- By the Artin Wedderburn theorem ( specifically, Wedderburn's part ), CSAs are all matrix algebras over a division algebra, and thus the quaternions are the only non-trivial division algebra over the reals.
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