Journal of the Australian Mathematical Society - Series A Vol. 65 Part 2 (1998) A note on uniform bounds of primeness in matrix rings John E. van den Berg Department of Mathematics and Applied Mathematics University of Natal Pietermaritzburg Private Bag X01 Scottsville 3209 South Africa Abstract: 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 Xof R we have $xXy\neq 0$ whenever $0\neq x,y\in R$. 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 $n\times n$ matrix ring over F. PDF file size: 77K © Copyright 1998, Australian Mathematical Society