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Abstract
It is know that a left quasi-morphic ring R is a ring of stable range 1 if and only if dim R = 0.
In this paper it is shown that a commutative morphic ring R is a ring of stable range 2 if and only if dimR= 1.
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References
2. Canfell M. J., Uniqueness of generators of principal ideals in rings of continuous function. Proc. Amer. Math. Soc., 26 (1970), 517--573.
3. Kaplansky I., Elementary divisirs and modules. Trans. Amer. Math. Soc., 66 (1949), 464--491.
4. Nicholson W.K., Sanchez Campos E. Rings with the dual of the isomorphism theorem. J. Algebra, 271 (2004), 391--406.
5. Siddique F., On two questions of Nicholson. arXiv: 1402.4706V1 [math. RA] 1S Feb 2014, 1-5.
6. Zabavsky B.V., Diagonal reduction of matrices over rings. Mathematical Studies, Monograph Series, v. XVI, VNTL Publishers, 2012, 251p.