Geodesic
Diagonalizability theorems for matrices over rings with finite stable range
Algebra and discrete mathematics, no. 1 (2005), pp. 151-165

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We construct the theory of diagonalizability for matrices over Bezout ring with finite stable range. It is shown that every commutative Bezout ring with compact minimal prime spectrum is Hermite. It is also shown that a principal ideal domain with stable range 1 is Euclidean domain, and every semilocal principal ideal domain is Euclidean domain. It is proved that every matrix over an elementary divisor ring can be reduced to “almost” diagonal matrix by elementary transformations.
Keywords: finite stable range, elementary divisor ring, Hermite ring, ring with elementary reduction of matrices, Bezout ring, minimal prime spectrum. 
@article{ADM_2005_1_a12,
     author = {Bogdan Zabavsky},
     title = {Diagonalizability theorems for matrices over rings with finite stable range},
     journal = {Algebra and discrete mathematics},
     pages = {151--165},
     publisher = {mathdoc},
     number = {1},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2005_1_a12/}
}
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Bogdan Zabavsky. Diagonalizability theorems for matrices over rings with finite stable range. Algebra and discrete mathematics, no. 1 (2005), pp. 151-165. http://geodesic.mathdoc.fr/item/ADM_2005_1_a12/