TY - JOUR

T1 - Commutative Bezout domains of stable range 1.5

AU - Bovdi, Victor A.

AU - Shchedryk, Volodymyr P.

N1 - Funding Information:
The authors are grateful for the referee's valuable remarks and suggestions. The research was supported by the UAEU UPAR grant G00002160.
Funding Information:
The authors are grateful for the referee's valuable remarks and suggestions. The research was supported by the UAEU UPAR grant G00002160 .
Publisher Copyright:
© 2018

PY - 2019/5/1

Y1 - 2019/5/1

N2 - A ring R is said to be of stable range 1.5 if for each a,b∈R and 0≠c∈R satisfying aR+bR+cR=R there exists r∈R such that (a+br)R+cR=R. Let R be a commutative domain in which all finitely generated ideals are principal, and let R be of stable range 1.5. Then each matrix A over R is reduced to Smith's canonical form by transformations PAQ in which P and Q are invertible and at least one of them can be chosen to be a product of elementary matrices. We generalize Helmer's theorem about the greatest common divisor of entries of A over R.

AB - A ring R is said to be of stable range 1.5 if for each a,b∈R and 0≠c∈R satisfying aR+bR+cR=R there exists r∈R such that (a+br)R+cR=R. Let R be a commutative domain in which all finitely generated ideals are principal, and let R be of stable range 1.5. Then each matrix A over R is reduced to Smith's canonical form by transformations PAQ in which P and Q are invertible and at least one of them can be chosen to be a product of elementary matrices. We generalize Helmer's theorem about the greatest common divisor of entries of A over R.

KW - Adequate ring

KW - Commutative Bezout domain

KW - Elementary divisor ring

KW - Stable range of a ring

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U2 - 10.1016/j.laa.2018.06.012

DO - 10.1016/j.laa.2018.06.012

M3 - Article

AN - SCOPUS:85048947239

VL - 568

SP - 127

EP - 134

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -