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Algebra and Discrete Mathematics, 2005, Issue 1, Pages 151–165
(Mi adm296)
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This article is cited in 10 scientific papers (total in 10 papers)
RESEARCH ARTICLE
Diagonalizability theorems for matrices over rings with finite stable range
Bogdan Zabavsky Ivan Franko National University of L'viv
Abstract:
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.
Received: 11.06.2004 Revised: 21.03.2005
Citation:
Bogdan Zabavsky, “Diagonalizability theorems for matrices over rings with finite stable range”, Algebra Discrete Math., 2005, no. 1, 151–165
Linking options:
https://www.mathnet.ru/eng/adm296 https://www.mathnet.ru/eng/adm/y2005/i1/p151
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Abstract page: | 252 | Full-text PDF : | 157 | First page: | 1 |
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