Ukrainian Mathematical Journal

, Volume 56, Issue 12, pp 2028–2034 | Cite as

Elementary Reduction of Matrices over Right 2-Euclidean Rings

  • O. M. Romaniv


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.


Stable Rank Elementary Reduction Bezout Ring Diagonal Reduction Hermite Ring 
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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • O. M. Romaniv
    • 1
  1. 1.Lviv National UniversityLvivUkraine

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