On Algebraic Shift Equivalence of Matrices over Polynomial Rings
| dc.creator | Chen, Sheng | |
| dc.date | 2007-10-19 | |
| dc.date | 2007-10-23 | |
| dc.date.accessioned | 2026-07-07T08:37:32Z | |
| dc.date.available | 2026-07-07T08:37:32Z | |
| dc.description | The 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.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/0710.3746 | |
| dc.identifier | http://arxiv.org/abs/0710.3746 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/140430 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Dynamical Systems | |
| dc.subject | 15A54; 15A23; 13C10; 37B10 | |
| dc.title | On Algebraic Shift Equivalence of Matrices over Polynomial Rings | |
| dc.type | text |