# Adequate properties of the elements with almost stable range 1 of a commutative elementary divisor domain

- Written by Bohdan Zabavsky
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Professor

Department of Algebra and Logic

Faculty of Mechanics and Mathematics

Ivan Franko National University of L'viv

**Abstract:**

*Let R — commutative elementary divisor domain which is not a ring of stable range 1. Then exist element a∈R with almost stable range 1 (i.e. for any elements b,c∈R such that aR+bR+cR=R exist elements r that aR+(br+c)R=R). In this report we describe algebraic properties these elements r∈R. Lets note that a commutative elementary divisor domain of stable range 1 is 2-Euclidean domain of stable range 1.*