Rings with Elementary Reduction of Matrices - Zabavskii, B. V.; Romaniv, A. M. (Ukrains’kyi Matematychnyi Zhurnal, 2000)
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.