Standard Bases over Rings
Afshan Sadiq
TL;DR
This paper develops the theory of standard bases for polynomial rings over a commutative Noetherian ring with solvable linear equations, extending concepts from fields to more general rings.
Contribution
It introduces a framework for standard bases over rings with local orderings, generalizing existing theories from fields to rings with solvable linear equations.
Findings
Established existence of standard bases over rings
Extended algorithms for polynomial ideal computations to rings
Provided conditions for solvability of linear equations in R
Abstract
The theory of standard bases in polynomial rings with coefficients in a ring R with respect to local orderings is developed. R is a commutative Noetherian ring with 1 and we assume that linear equations are solvable in R.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Topics in Algebra · Rings, Modules, and Algebras