2024/12/10 by Mohamed Mahmoud Chems-Eddin, B. Feryouch, Chems-Eddin, Mohamed Mahmoud +5
Mathematics · Computer Science · #Rings, Modules, and Algebras #Commutative Algebra and Its Applications #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2412.07931
Let D be an integral domain with quotient field K and E a subset of K. The ring of integer-valued rational functions on E is defined as intR(E,D):=\lbrace φ∈ K(X); φ(E)⊆ D\rbrace. The main goal of this paper is to investigate the Krull dimension of the ring intR(E,D). Particularly, we are interested in domains that are either Jaffard or PVDs. Interesting results are established with some illustrating examples.