Abstract
Let Λ be an associative ring with 1 and let б be a net of ideals in Λ of ordern. A net subgroup G(б) in the general linear group GL(n,Λ) is defined to be the largest subgroup in the multiplicative system e+M(б), where M (б) is a subring in the ring of matrices M(n,Λ) associated with б and e is the unit matrix. This implies that an invertible matrix x, is contained in G(б) if and only if both the matrices x and x−1 are contained in e+M(б). The question arises: for which rings is the second of these conditions a consequence of the first?
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