Let F be a field of which alpha, beta are components. Is it possible for (alpha)x(beta)=0, if alpha and beta are both nonzero?
Any ideas? Thanks for your help.
Originally Posted by Swlabr
Surely the point of this question is to prove that it is an integral domain.
To prove this result you should use the fact that every non-zero element has an inverse combined with the fact that zero does not have an inverse.
Really? Ok. First note that every field, by definition, is a commutative division ring. And thus, exists. So . But, it is relatively easy to see that and thus .
Really? Ok. First note that every field, by definition, is a commutative division ring. And thus, exists. So . But, it is relatively easy to see that and thus .