Reference 
1. W.K. Nicholson, Lifting idempotent and exchange rings, Trans. Amer. Math. Soc., 229 (1977), 269–278.
2. B.V. Zabavskii, N.Ya. Komarnitskii, Distributive elementary divisor domains, Ukr. Mat. Zh., 42 (1990),
¹7, 1000–1004. (in Russian)
3. I. Kaplansky, Elementary divisors and modules, Trans. Amer. Math. Soc., 66 (1949), 464–491.
4. M. Henriksen, On a class of regular rings that are elementary divisor rings, Arch. Math., 24 (1973), ¹2,
133–141.
5. B.V. Zabavsky, Diagonalization of matrices over ring with finite stable range, Visn. L’viv Univ. Ser.
Mekh.Mat., 61 (2003), 206–210.
6. H. Chen, Rings with many idempotents, Internat. J. Math., 22 (1999), ¹3, 547–558.
7. A.A. Tuganbaev, Rings of elementary divisors and distributive rings, Russian Mathematical Surveys, 46
(1991), ¹6, 230–231.
8. P.M. Cohn, Some remarks on projectivefree rings, Algebra univers., 49 (2009), 159–164.
9. G. Song, X. Guo, Diagonability of idempotent matrices over noncomutative rings, Linear Algebra and its
Appl., 297 (1999), 1–7.
