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Ukrainian Mathematical Journal

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

Elementary Reduction of Matrices over Right 2-Euclidean Rings

  • O. M. Romaniv
Article

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.

Keywords

Stable Rank Elementary Reduction Bezout Ring Diagonal Reduction Hermite Ring 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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