Anisotropic modules over artinian principal ideal rings

Details Anisotropic modules over artinian principal ideal rings Anisotropic modules over artinian principal ideal rings

2011-09-29

arxiv.org/abs/1109.6483v1

Mathematics

Commutative Algebra

18 pages

Scientific paper

Let V be a finite-dimensional vector space over a field k and let W be a 1-dimensional k-vector space. Let < , >: V x V \to W be a symmetric bilinear form. Then < , > is called anisotropic if for all nonzero v \in V we have \neq 0. Motivated by a problem in algebraic number theory, we come up with a generalization of the concept of anisotropy to symmetric bilinear forms on finitely generated modules over artinian principal ideal rings. We will give many equivalent definitions of this concept of anisotropy. One of the definitions shows that one can check if a form is anisotropic by checking if certain forms on vector spaces are anisotropic. We will also discuss the concept of quasi-anisotropy of a symmetric bilinear form, which has no useful vector space analogue. Finally we will discuss the radical root of a symmetric bilinear form, which doesn't have a useful vector space analogue either. All three concepts have applications in algebraic number theory.

Affiliated with

Also associated with

No associations

Rating

Anisotropic modules over artinian principal ideal rings 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 Anisotropic modules over artinian principal ideal rings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Anisotropic modules over artinian principal ideal rings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-151717