Unipotent similarity for matrices over commutative domains

A unit u of a ring is called unipotent if u − 1 is nilpotent. We characterize the similarity of 2×2 matrices over commutative domains, realized by unipotent matrices, i.e., B = U−1AU with unipotent matrix U.

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Publication Details

Journal
Acta Universitatis Sapientiae Mathematica
Published
2025-02-19
DOI
https://doi.org/10.47745/ausm-2024-0006
Primary Topic
Rings, Modules, and Algebras
Type
article
Field-Weighted Citation Impact
0.00
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article

Unipotent similarity for matrices over commutative domains

Grigore Călugăreanu
Acta Universitatis Sapientiae Mathematica
Rings, Modules, and Algebras
article

Unipotent similarity for matrices over commutative domains

Grigore Călugăreanu
article en

Abstract

A unit u of a ring is called unipotent if u − 1 is nilpotent. We characterize the similarity of 2×2 matrices over commutative domains, realized by unipotent matrices, i.e., B = U−1AU with unipotent matrix U.

Acta Universitatis Sapientiae MathematicaVol. 16(1)
Openalex Percentile: Top 91%
Rings, Modules, and Algebras
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Unipotent similarity for matrices over commutative domains — Grigore Călugăreanu · Acta Universitatis Sapientiae Mathematica (2025) | TGRS Research Map | TGRS