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One-Sided Inverses in Rings

Published online by Cambridge University Press:  20 November 2018

Roger D. Peterson
Roger D. Peterson*
Affiliation:
University of Wisconsin-Milwaukee, Milwaukee, Wisconsin
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Following Herstein [2], we will call a ring R with identity von Neumann finite (vNf) provided that xy = 1 implies yx — WnR. Kaplansky [4] showed that group algebras over fields of characteristic zero are vNf rings, and further, that full matrix rings over such rings are also vNf. Herstein [2] has posed the problem for group algebras over fields of arbitrary characteristic. If group algebras over fields are always vNf, then it is easily seen that group algebras over commutative rings are always vNf. What conditions on the underlying ring of scalars would force the vNf property for all group rings over it?

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 1 , 01 February 1975 , pp. 218 - 224
Copyright
Copyright © Canadian Mathematical Society 1975

References

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