Rings with Elementary Reduction of Matrices
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.
English version (Springer): Ukrainian Mathematical Journal 52 (2000), no. 12, pp 1872-1881.
Citation Example: Romaniv A. M., Zabavskii B. V. Rings with Elementary Reduction of Matrices // Ukr. Mat. Zh. - 2000. - 52, № 12. - pp. 1641-1649.