Geodesic
Quasi-Euclidean duo rings with elementary reduction of matrices
Algebra and discrete mathematics, Tome 20 (2015) no. 2, pp. 317-324

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We establish necessary and sufficient conditions under which a class of quasi-Euclidean duo rings coincides with a class of rings with elementary reduction of matrices. We prove that a Bezout duo ring with stable range 1 is a ring with elementary reduction of matrices. It is proved that a semiexchange quasi-duo Bezout ring is a ring with elementary reduction of matrices iff it is a duo ring.
Keywords: Bezout ring, duo ring, stable range, semiexchange ring, ring with elementary reduction of matrices. 
@article{ADM_2015_20_2_a8,
     author = {O. Romaniv and A. Sagan},
     title = {Quasi-Euclidean duo rings with elementary reduction of matrices},
     journal = {Algebra and discrete mathematics},
     pages = {317--324},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2015_20_2_a8/}
}
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O. Romaniv; A. Sagan. Quasi-Euclidean duo rings with elementary reduction of matrices. Algebra and discrete mathematics, Tome 20 (2015) no. 2, pp. 317-324. http://geodesic.mathdoc.fr/item/ADM_2015_20_2_a8/