Factorial and Noetherian Subrings of Power Series Rings

Details Factorial and Noetherian Subrings of Power Series Rings Factorial and Noetherian Subrings of Power Series Rings

2009-10-21

arxiv.org/abs/0910.3999v1

Mathematics

Algebraic Geometry

13 pages

Scientific paper

Let $F$ be a field. We show that certain subrings contained between the polynomial ring $F[X] = F[X_1, ..., X_n]$ and the power series ring $F[X][[Y]] = F[X_1, ..., X_n][[Y]]$ have Weierstrass Factorization, which allows us to deduce both unique factorization and the Noetherian property. These intermediate subrings are obtained from elements of $F[X][[Y]]$ by bounding their total $X$-degree above by a positive real-valued monotonic up function $\lambda$ on their $Y$-degree. These rings arise naturally in studying $p$-adic analytic variation of zeta functions over finite fields. Future research into this area may study more complicated subrings in which $Y = (Y_1, >..., Y_m)$ has more than one variable, and for which there are multiple degree functions, $\lambda_1, ..., \lambda_m$. Another direction of study would be to generalize these results to $k$-affinoid algebras.

Affiliated with

Also associated with

No associations

Rating

Factorial and Noetherian Subrings of Power Series 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 Factorial and Noetherian Subrings of Power Series Rings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Factorial and Noetherian Subrings of Power Series Rings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-143637