An algebra with a reciprocal that behaves like in the rational and real numbers.
A reciprocal algebra is a possibly non-associative algebra , typically over a field , which has the property that for non-zero element , there exists an element , called the reciprocal of , such that for every element
Every Cayley-Dickson algebra is a reciprocal algebra. Examples include the real numbers , the complex numbers , the quaternions , and the octonions .
The ring of rational polynomials is a real reciprocal algebra.
There exists a reciprocal algebra with nonzero zero divisors.
Last revised on August 23, 2024 at 15:37:59. See the history of this page for a list of all contributions to it.