Rings with Elementary Reduction of Matrices

  • B. V. Zabavskii
  • A. M. Romaniv

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.
Published
25.12.2000
How to Cite
ZabavskiiB. V., and RomanivA. M. “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.
Section
Research articles