division algebra वाक्य

उदाहरण वाक्य

1. 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.
2. 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.
3. "' Frobenius theorem "': The only finite-dimensional associative division algebras over the reals are the reals themselves, the complex numbers, and the quaternions.
4. By the Cayley Hamilton theorem, 0 } } and because is a division algebra, it follows that either 0 } } for some or that 0 } } for some.
5. A " finite-dimensional " unital associative algebra ( over any field ) is a division algebra " if and only if " it has no zero divisors.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.