2011•Unpublished venueRequires access

On Square Matrices with Stable Entries

Huanyin Chen

Abstract

This paper extended stable rings to ideals of a ring,and investigated matrices with stable entries.The results prove that every square matrix with 1 stable entries over an exchange ring admits a diagonal reduction,and that every square matrix with unit 1 stable entries is a sum of two invertible matrices.The paper obtained an analogous result by square matrices with 2 stable entries,and studied triangular decompositions of square matrices with stable entries.

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Key concepts: Square (algebra), Square matrix, Invertible matrix, Mathematics, Diagonal, Ring (chemistry), Matrix (chemical analysis), Unit (ring theory)