Turkish Journal of Mathematics
Article Title
DOI
10.3906/mat-1502-58
Abstract
We combine Euclidean and adequate rings, and introduce a new type of ring. A ring $R$ is called an E-adequate ring provided that for any $a,b\in R$ such that $aR+bR=R$ and $c\neq 0$ there exists $y\in R$ such that $(a+by,c)$ is an E-adequate pair. We shall prove that an E-adequate ring is an elementary divisor ring if and only if it is a Hermite ring. Elementary matrix reduction over such rings is also studied. We thereby generalize Domsha, Vasiunyk, and Zabavsky's theorems to a much wider class of rings.
First Page
506
Last Page
516
Recommended Citation
CHEN, HUANYIN and SHEIBANI, MARJAN
(2016)
"Combining Euclidean and adequate rings,"
Turkish Journal of Mathematics: Vol. 40:
No.
3, Article 3.
https://doi.org/10.3906/mat-1502-58
Available at:
https://journals.tubitak.gov.tr/math/vol40/iss3/3
