transfinite arithmetic, cardinal arithmetic, ordinal arithmetic
prime field, p-adic integer, p-adic rational number, p-adic complex number
arithmetic geometry, function field analogy
Given a star-algebra in characteristic zero, then for any element
its real part is ;
its imaginary part is ,
where is the given star-anti-involution (e.g. complex conjugation, quaternionic conjugation, …).
Standard situations where real and imaginary parts are considered include the real normed division algebra
the complex numbers;
the quaternions;
the octonions
Last revised on January 26, 2021 at 12:19:33. See the history of this page for a list of all contributions to it.