Generators of maximal orders

Rostyslav Kravchenko, Marcin Mazur*, Bogdan V. Petrenko

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Let R be the ring of algebraic integers in a number field K and let Λ be a maximal order in a finite dimensional semisimple K-algebra B. Building on our previous work [3], we compute the smallest number of algebra generators of Λ 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.

Original languageEnglish (US)
Pages (from-to)32-50
Number of pages19
JournalJournal of Algebra
StatePublished - Mar 5 2015


  • Generators of algebras
  • Maximal orders
  • Smallest number of generators

ASJC Scopus subject areas

  • Algebra and Number Theory


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