Elementary matrix reduction over certain rings |
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| Authors: | Marjan Sheibani Rahman Bahmani |
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| Affiliation: | Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran |
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| Abstract: | We explore elementary matrix reduction over certain rings characterized by properties related to stable range. Let R be a commutative ring. We call R locally stable if aR+bR = R??x∈R such that R∕(a+bx)R has stable range 1. We study locally stable rings and prove that every locally stable Bézout ring is an elementary divisor ring. Many known results on domains are thereby generalized. |
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| Keywords: | Elementary divisor ring localization locally stable ring stable range 1 |
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