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arXiv · 1406.6465

Generators of maximal orders

Rostyslav V. Kravchenko·Marcin Mazur·Bogdan V. Petrenko
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Abstract

Let R be the ring of algebraic integers in a number field K and let L be a maximal order in a semisimple K-algebra B. Building on our previous work, we compute the smallest number of algebra generators of L considered as an R-algebra. This reproves and vastly extends the results of P.A.B. Pleasants, who considered the case when B is a number field. In order to achieve our goal, we obtain several results about counting generators of algebras which have finitely many elements. These results should be of independent interest.

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Rostyslav V. Kravchenko, Marcin Mazur, Bogdan V. Petrenko. 2014-06-25. Generators of maximal orders. https://arxiv.org/abs/1406.6465

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