Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $\alpha \in \mathbb{A}$, and $\gamma \in \mathbb{T}$. I know that the reciprocal of a transcendental number is transcendental.


Is $\alpha\cdot \gamma \in \mathbb{T}$?

share|cite|improve this question
This works for many "number systems". See this answer, for a general viewpoint. – Bill Dubuque Aug 17 '14 at 16:54
@BillDubuque Thanks Bill Dubuque, It is excellent reference. – kaka Aug 17 '14 at 19:37
up vote 12 down vote accepted
  • No if $\alpha=0$ (because then you get $0$ which is algebraic)
  • Yes if $\alpha \neq 0$ (because if $\alpha \gamma$ is algebraic, then also $\alpha^{-1} \alpha \gamma = \gamma$ would be algebraic)
share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.