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
UR - http://www.scopus.com/inward/record.url?scp=85048947239&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85048947239&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2018.06.012
DO - 10.1016/j.laa.2018.06.012
M3 - Article
AN - SCOPUS:85048947239
SN - 0024-3795
VL - 568
SP - 127
EP - 134
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -