Rings with Elementary Reduction of Matrices

Authors

  • 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

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.