J. Aust. Math. Soc.
76 (2004), 167174

On uniform bounds of primeness in matrix rings

Konstantin I. Beidar
Department of Mathematics
National Cheng Kung University
Tainan
Taiwan
beidar@mail.ncku.edu.tw





Abstract

A subset of an associative
ring is a uniform insulator
for provided for any
nonzero . The ring is called uniformly strongly prime of bound
if has uniform insulators and the smallest of those
has cardinality . Here we compute these bounds for matrix rings
over fields and obtain refinements of some
results of van den Berg in this context. More
precisely, for a field and a positive
integer , let be the bound of the matrix
ring , and
let be , where
is a subspace
of of maximal dimension with respect to not
containing rank one matrices. We show
that . This implies, for
example, that if and only if there exists a (nonassociative)
division algebra over of dimension .

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