Abstract
We present some variants of the Kaplansky condition for a K-Hermite ring R to be an elementary divisor ring. For example, a commutative K-Hermite ring R is an EDR iff for any elements x,y, z Ie{cyrillic, ukrainian} R such that (x, y) = R there exists an element λ Ie{cyrillic, ukrainian} R such that x + λy = uv, where (u,z) = (v, 1 - z) = R. We present an example of a Bezout domain that is an elementary divisor ring but does not have almost stable range 1, thus answering a question of Warren Wm. McGovern.
Original language | English |
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Pages (from-to) | 3013-3018 |
Number of pages | 6 |
Journal | Proceedings of the American Mathematical Society |
Volume | 141 |
Issue number | 9 |
DOIs | |
State | Published - 2013 |
Keywords
- Almost stable range 1
- Elementary divisor ring
- K-Hermite
- Kaplansky condition
- Stable range
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics