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On unit stable range one matrices

2021/04/08 by Grigore Călugăreanu, Calugareanu, Grigore
Computer Science · Mathematics · #15B33 #15B36 #16U10 #16U60 #16U99 #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2104.03994

openalex publication_date 2021/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize the unit stable range one 2x2 and 3x3 matrices over commutative rings. In particular, we characterize the 2x2 matrices which satisfy the Goodearl-Menal condition. For 2x2 integral matrices we show that the stable range one and the unit stable range one properties are equivalent, and, that the only matrix which satisfies the Goodearl-Menal condition is the zero matrix.

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