Abstract
Let A be a ring such that all maximal indecomposable factor rings Ai of A are serial rings. Then every square matrix over A is diagonalizable. In addition, if all the rings Ai are Bezout rings, then every rectangular matrix over A is diagonalizable. If ϕ is an automorphism of the ring A, then the skew Laurent series ring A((x, ϕ)) is a serial ring if and only if A is a serial Artinian ring.
Originally published in Diskretnaya Matematika (2016) 28, №4, 150–157 (in Russian).
Funding source: Russian Science Foundation
Award Identifier / Grant number: 16-11-10013
Funding statement: The study is supported by Russian Science Foundation (project no. 16-11-10013)
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