2019/07/03 by Steven Dale Cutkosky, Cutkosky, Steven Dale, Josnei Novacoski +1
Mathematics · #Advanced Topics in Algebra #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1907.01859
openalex publication_date 2019/07/03 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
The main goal of this paper is to study some properties of an extension of\nvaluations from classical invariants. More specifically, we consider a valued\nfield (K,\ν) and an extension \ω of \ν to a finite extension L of\nK. Then we study when the valuation ring of \ω is essentially finitely\ngenerated over the valuation ring of \ν. We present a necessary condition in\nterms of classic invariants of the extension by Hagen Knaf and show that in\nsome particular cases, this condition is also sufficient. We also study when\nthe corresponding extension of graded algebras is finitely generated. For this\nproblem we present an equivalent condition (which is weaker than the one for\nthe finite generation of the valuation rings).\n