On Algebraic Shift Equivalence of Matrices over Polynomial Rings

dc.creatorChen, Sheng
dc.date2007-10-19
dc.date2007-10-23
dc.date.accessioned2026-07-07T08:37:32Z
dc.date.available2026-07-07T08:37:32Z
dc.descriptionThe paper studies algebraic strong shift equivalence of matrices over $n$-variable polynomial rings over a principal ideal domain $D$($n\leq 2$). It is proved that in the case $n=1$, every non-zero matrix over $D[x]$ has a full rank factorization and every non-nilpotent matrix over $D[x]$ is algebraically strong shift equivalent to a nonsingular matrix. In the case $n=2$, an example of non-nilpotent matrix over $\mathbb{R}[x,y,z]=\mathbb{R}[x][y,z]$, which can not be algebraically shift equivalent to a nonsingular matrix, is given.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/0710.3746
dc.identifierhttp://arxiv.org/abs/0710.3746
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/140430
dc.subjectRings and Algebras
dc.subjectDynamical Systems
dc.subject15A54; 15A23; 13C10; 37B10
dc.titleOn Algebraic Shift Equivalence of Matrices over Polynomial Rings
dc.typetext

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