Splitting full matrix algebras over algebraic number fields

Details Splitting full matrix algebras over algebraic number fields Splitting full matrix algebras over algebraic number fields

2011-06-30

arxiv.org/abs/1106.6191v3

Mathematics

Rings and Algebras

15 pages; Theorem 2 and Lemma 8 corrected

Scientific paper

Let K be an algebraic number field of degree d and discriminant D over Q. Let A be an associative algebra over K given by structure constants such that A is isomorphic to the algebra M_n(K) of n by n matrices over K for some positive integer n. Suppose that d, n and D are bounded. Then an isomorphism of A with M_n(K) can be constructed by a polynomial time ff-algorithm. (An ff-algorithm is a deterministic procedure which is allowed to call oracles for factoring integers and factoring univariate polynomials over finite fields.) As a consequence, we obtain a polynomial time ff-algorithm to compute isomorphisms of central simple algebras of bounded degree over K.

Affiliated with

Also associated with

No associations

Rating

Splitting full matrix algebras over algebraic number fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Splitting full matrix algebras over algebraic number fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Splitting full matrix algebras over algebraic number fields will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-34993