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- Title
Cohen-type theorem for adequacy and elementary divisor rings.
- Authors
Zabavs'kyi, B. V.; Komarnyts'kyi, M. Ya.
- Abstract
We introduce the notion of a relatively adequate element of a commutative ring, which is not necessary a domain, investigate properties of such elements, and on the basis of this, propose the characterization of absolutely adequate elements. In particular, we prove that an adequate Bezout ring has a stable rank that is not higher than 2. As a consequence, it is stated that the adequate Bezout ring is a ring of elementary divisors.
- Subjects
RING theory; RINGS with divided powers; COHEN-Macaulay rings; COMMUTATIVE rings; SMALL divisors
- Publication
Journal of Mathematical Sciences, 2010, Vol 167, Issue 1, p107
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-010-9906-0