Diagonal reduction of matrices over Bezout rings of stable range 1 with the Kazimirsky condition

2019/03/24 by Bohdan Zabavsky, Zabavsky, Bohdan, Oleh Romaniv +1
Mathematics · #06F20 #13F99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1903.10049

openalex publication_date 2019/03/24 · openalex created_date 2019/04/01 · openalex updated_date 2026/07/28

Abstract

We constuct the theory of diagonalizability for matrices over Bezout rings of stable range 1 with the Kazimirsky condition. It is shown that a ring of stable range 1 with the right (left) Kazimirsky condition is an elementary divisor ring if and only if it is a duo ring.

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