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math.RA2018
J-Noetherian Bezout domain which is not a ring of stable range 1
Bohdan Zabavsky, Oleh Romaniv
We proved that in J-Noetherian Bezout domain which is not a ring of stable range 1 exists a nonunit adequate element (element of almost stable range 1
math.RA2018
A Bezout ring of stable range 2 which has square stable range 1
Bohdan Zabavsky, Oleh Romaniv
In this paper we introduced the concept of a ring of stable range 2 which has square stable range 1. We proved that a Hermitian ring which has (right) square stable range 1 is…
math.RA2018
Diagonal reduction of matrices over commutative semihereditary Bezout rings
Bohdan Zabavsky, Andry Gatalevych
It is proven that every commutative semihereditary Bezout ring in which any regular element is Gelfand (adequate), is an elementary divisor ring.