# Stable range conditions for abelian and duo rings

- Written by A. Gatalevych, A. Dmytruk
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*Associate Professor**Department of Algebra and Logic**Faculty of Mechanics and Mathematics** Ivan Franko National University of L'viv*

*Department of Algebra and Logic**Faculty of Mechanics and Mathematics** Ivan Franko National University of L'viv*

**Abstract:**

*We introduce the concepts of a ring of (von Neumann) regular range 1, a ring of semihereditary range 1, a ring of regular range 1. We find relationships between the introduced classes of rings and known ones for abelian and duo rings. We proved that Hermite duo ring of Gelfand range 1 is an elementary divisor ring.*

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