An embedding property of universal division algebras

Zinovy Reichstein, Nikolaus Vonessen

Research output: Contribution to journalArticlepeer-review

Abstract

Let A be a central simple algebra of degree n and let k be a subfield of its center. We show that A contains a copy of the universal division algebra Dm, n(k) generated by m generic n × n matrices if and only if trdegkA ≥ trdegkDm, n(k) = (m - 1)n2 + 1. Moreover, if in addition the center of A is finitely and separately generated over k then “almost all” division subalgebras of A generated by m elements are isomorphic to Dm, n(k). In the last section we give an application of our main result to the question of embedding free groups in division algebras.

Original languageEnglish
Pages (from-to)451-462
Number of pages12
JournalJournal of Algebra
Volume177
Issue number2
DOIs
StatePublished - Oct 15 1995

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