Non-commutative Characteristic Polynomials and Cohn Localization
| dc.creator | Sheiham, Desmond | |
| dc.date | 2001-04-15 | |
| dc.date.accessioned | 2026-07-07T04:41:20Z | |
| dc.date.available | 2026-07-07T04:41:20Z | |
| dc.description | Almkvist proved that for a commutative ring A the characteristic polynomial of an endomorphism α:P \to P of a finitely generated projective A-module determines (P,α) up to extensions. For a non-commutative ring A the generalized characteristic polynomial of an endomophism α: P \to P of a finitely generated projective A-module is defined to be the Whitehead torsion [1-xα] \in K_1(A[[x]]), which is an equivalence class of formal power series with constant coefficient 1. In this paper an example is given of a non-commutative ring A and an endomorphism α:P \to P for which the generalized characteristic polynomial does not determine (P,α) up to extensions. The phenomenon is traced back to the non-injectivity of the natural map Σ^{-1}A[x] \to A[[x]], where Σ^{-1}A[x] is the Cohn localization of A[x] inverting the set Σof matrices in A[x] sent to an invertible matrix by A[x] \to A; x \mapsto 0. | |
| dc.description | 18 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/math/0104158 | |
| dc.identifier | http://arxiv.org/abs/math/0104158 | |
| dc.identifier | Journal of the London Mathematical Society (2) Vol 64 (2001) no.1 pp13-28 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61312 | |
| dc.subject | Rings and Algebras | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 16S34;18F25 | |
| dc.title | Non-commutative Characteristic Polynomials and Cohn Localization | |
| dc.type | text |