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arXiv · 1412.5714

Elementary Matrix Reduction Over J-Stable Rings

Marjan Sheibani Abdolyousefi·Huanyin Chen
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Abstract

A commutative ring $R$ is J-stable provided that for any $a\not\in J(R)$, $R/aR$ has stable range one. A ring $R$ is called an elementary divisor ring if every $m\times n$ matrix over $R$ admits diagonal reduction. We prove that a J-stabe ring $R$ is an elementary divisor ring if and only if it is a Bezout ring.

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Marjan Sheibani Abdolyousefi, Huanyin Chen. 2014-12-18. Elementary Matrix Reduction Over J-Stable Rings. https://arxiv.org/abs/1412.5714

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