Elementary Reduction of Matrices over Right 2-Euclidean Rings

  • A. M. Romaniv

Abstract

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.
Published
25.12.2004
How to Cite
RomanivA. M. “Elementary Reduction of Matrices over Right 2-Euclidean Rings”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, no. 12, Dec. 2004, pp. 1717 -, https://umj.imath.kiev.ua/index.php/umj/article/view/3879.
Section
Short communications