Rings with Elementary Reduction of Matrices
Abstract
We establish necessary and sufficient conditions under which a quasi-Euclidean ring coincides with a ring with elementary reduction of matrices. We prove that a semilocal Bézout ring is a ring with elementary reduction of matrices and show that a 2-stage Euclidean domain is also a ring with elementary reduction of matrices. We formulate and prove a criterion for the existence of solutions of a matrix equation of a special type and write these solutions in an explicit form.Downloads
Published
25.12.2000
Issue
Section
Research articles
How to Cite
Zabavskii, B. V., and A. M. Romaniv. “Rings With Elementary Reduction of Matrices”. Ukrains’kyi Matematychnyi Zhurnal, vol. 52, no. 12, Dec. 2000, pp. 1641-9, https://umj.imath.kiev.ua/index.php/umj/article/view/4568.