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- W2147383718 abstract "Abstract A subset S of an associative ring R is a uniform insulator for R provided a S b ≠ 0 for any nonzero a, b ∈ R . The ring R is called uniformly strongly prime of bound m if R has uniform insulators and the smallest of those has cardinality m . 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 F and a positive integer k , let m be the bound of the matrix ring M k (F) , and let n be dim F ( V ), where V is a subspace of M k (F) of maximal dimension with respect to not containing rank one matrices. We show that m + n = k 2 . This implies, for example, that n = k 2 − k if and only if there exists a (nonassociative) division algebra over F of dimension k ." @default.
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- W2147383718 date "2004-04-01" @default.
- W2147383718 modified "2023-09-23" @default.
- W2147383718 title "On uniform bounds of primeness in matrix rings" @default.
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- W2147383718 doi "https://doi.org/10.1017/s1446788700008879" @default.
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