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A note on uniform bounds of primeness in matrix rings

Part of: Jordan algebras Radicals and radical properties of rings

Published online by Cambridge University Press:  09 April 2009

John E. Van den Berg
John E. Van den Berg
Affiliation:
Department of Mathematics and Applied Mathematics, University of Natal Pietermaritzburg, Private Bag X01, Scottsville 3209, South Africa e-mail: [email protected]
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Abstract

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A nonzero ring R is said to be uniformly strongly prime (of bound n) if n is the smallest positive integer such that for some n-element subset X of R we have xXy ≠ 0 whenever 0 ≠ x, y ∈ R. The study of uniformly strongly prime rings reduces to that of orders in matrix rings over division rings, except in the case n = 1. This paper is devoted primarily to an investigation of uniform bounds of primeness in matrix rings over fields. It is shown that the existence of certain n-dimensional nonassociative algebras over a field F decides the uniform bound of the n × n matrix ring over F.

MSC classification

Secondary: 16N60: Prime and semiprime rings 17C55: Finite-dimensional structures 17C60: Division algebras
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 65 , Issue 2 , October 1998 , pp. 212 - 223
Copyright
Copyright © Australian Mathematical Society 1998

References

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