11 votes

Is it decidable whether two real algebraic irrationals generate the same extension of the rationals?

Indeed there are algorithms for factoring $f_\beta$ over $\mathbb Q(\alpha)$, and the number of linear factors gives the number of distinct roots of $f_\beta$ in $\mathbb Q(\alpha)$ (and their ...
Russell Miller's user avatar
11 votes
Accepted

Is it decidable whether two real algebraic irrationals generate the same extension of the rationals?

Yes, there are algorithms for factoring $f_\beta$ over the number field $\mathbb{Q}(\alpha)$; if a linear factor is found and both irreducible polynomials have the same degree, then $\mathbb{Q}(\alpha)...
GNiklasch's user avatar
  • 2,391
9 votes
Accepted

Unique factorization of ideals in a quadratic field

It is not true that $(\alpha)$ is the product of distinct ramified primes. What is true is that there exists an $\alpha\in\mathcal{O}_k$ satisfying $(1)$ for which $(\alpha)$ is the product of ...
GH from MO's user avatar
  • 99.1k
4 votes

Characters on ray class groups

The question makes no sense as it stands, because $\chi$ and $\psi$ are characters on different groups (so it makes no sense to multiply them). Also, I think that the property "$\alpha$ is ...
GH from MO's user avatar
  • 99.1k
3 votes
Accepted

Hansel's simple proof of the Skolem Mahler Lech theorem

What you found is essentially a research announcement; publishing these seems to be common practice in computer science. The full paper was published the next year in Theoretical Computer Science, ...
Brian Hopkins's user avatar
3 votes

Artin-Schreier theorem for rings (a little different)

I am assuming that you intended for $R$ to already be integrally closed in $K$, i.e. normal. Then the answer to your question is yes. Claim: Suppose the domain $R$ is integrally closed in its field of ...
Manny Reyes's user avatar
  • 5,142
3 votes

Is there something I am missing about the computation of the $p$-part of the class groups of cyclotomic fields?

Recently, I stumbled coincidentally on the paper Computation of invariants in the theory of cyclotomic fields K. Iwasawa and C. Sims J. Math. Soc. Japan Vol.18 (1966) This explains in full details how ...
Olivier's user avatar
  • 10.3k

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