Elementary Reduction of Matrices over Right 2-Euclidean Rings
We introduce a concept of noncommutative (right) 2-Euclidean ring. We prove that a 2-Euclidean ring is a right Hermite ring, a right Bezout ring, and a GE n -ring. It is shown that an arbitrary right unimodular string of length not less than 3 over a right Bezout ring of stable rank possesses an elementary diagonal reduction. We prove that a right Bezout ring of stable rank 1 is a right 2-Euclidean ring.
English version (Springer): Ukrainian Mathematical Journal 56 (2004), no. 12, pp 2028-2034.
Citation Example: Romaniv A. M. Elementary Reduction of Matrices over Right 2-Euclidean Rings // Ukr. Mat. Zh. - 2004. - 56, № 12. - pp. 1717 – 1721.