Elementary matrix reduction over locally stable rings

Abstract

A commutative ring R is locally stable provided that for any a,b∈ R such that aR+bR=R, there exist some y∈ R such that R/(a+by)R has stable range 1.For a Bezout ring R, we prove that R is an elementary divisor ring if and only if R is locally stable if and only if R has neat range 1.

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