Author： Zabavs’kyi B. Komarnyts’kyi M.
Publisher： Springer Publishing Company
ISSN： 1072-3374
Source： Journal of Mathematical Sciences, Vol.167, Iss.1, 2010-05, pp. : 107-111
Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.
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.
Related content
A Cohen-type theorem for Artinian modules
Archiv der Mathematik, Vol. 87, Iss. 3, 2006-09 ,pp. :
Access to resources
Recommend
Rings with Elementary Reduction of Matrices
By Zabavskii B.V. Romaniv O.M.
Ukrainian Mathematical Journal, Vol. 52, Iss. 12, 2000-12 ,pp. :
Siberian Mathematical Journal, Vol. 45, Iss. 3, 2004-05 ,pp. :
An Elementary Proof of Marden's Theorem
By Kalman Dan
American Mathematical Monthly, Vol. 115, Iss. 4, 2008-04 ,pp. :