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Von Neumann finite endomorphism rings

Authors
Journal
Indagationes Mathematicae
0019-3577
Publisher
Elsevier
Publication Date
Volume
14
Issue
2
Identifiers
DOI: 10.1016/s0019-3577(03)90006-1

Abstract

Abstract Let K be a field of characteristic zero, G a group acting on a nonempty set X and KX the permutation module induced by this action. By studying traces of idempotents, we prove that the endomorphism ring End K[ G] ( KX) is von Neumann finite under certain conditions for the action of G on X. This generalizes a classical result by Kaplansky for the group ring of G over K.

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