Non-commutative Characteristic Polynomials and Cohn Localization

Details Non-commutative Characteristic Polynomials and Cohn Localization Non-commutative Characteristic Polynomials and Cohn Localization

2001-04-15

arxiv.org/abs/math/0104158v1

Journal of the London Mathematical Society (2) Vol 64 (2001) no.1 pp13-28

Mathematics

Rings and Algebras

18 pages, LaTeX

Scientific paper

Almkvist proved that for a commutative ring A the characteristic polynomial of an endomorphism \alpha:P \to P of a finitely generated projective A-module determines (P,\alpha) up to extensions. For a non-commutative ring A the generalized characteristic polynomial of an endomophism \alpha : P \to P of a finitely generated projective A-module is defined to be the Whitehead torsion [1-x\alpha] \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 \alpha:P \to P for which the generalized characteristic polynomial does not determine (P,\alpha) up to extensions. The phenomenon is traced back to the non-injectivity of the natural map \Sigma^{-1}A[x] \to A[[x]], where \Sigma^{-1}A[x] is the Cohn localization of A[x] inverting the set \Sigma of matrices in A[x] sent to an invertible matrix by A[x] \to A; x \mapsto 0.

Affiliated with

Also associated with

No associations

Rating

Non-commutative Characteristic Polynomials and Cohn Localization does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Non-commutative Characteristic Polynomials and Cohn Localization, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Non-commutative Characteristic Polynomials and Cohn Localization will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-263607