Geodesic
Bezout rings without non-central idempotents
Diskretnaya Matematika, Tome 28 (2016) no. 2, pp. 133-145.

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Let $A$ be a Bezout ring without non-central idempotents. If $A$ is a right or left Rickartian ring, then $A$ is an Hermitian ring. If $A$ is an exchange ring, then every rectangular matrix over $A$ is diagonalizable.
Keywords: Bezout ring, Hermitian ring, diagonalizable ring. 
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A. A. Tuganbaev. Bezout rings without non-central idempotents. Diskretnaya Matematika, Tome 28 (2016) no. 2, pp. 133-145. http://geodesic.mathdoc.fr/item/DM_2016_28_2_a12/

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