Flow-up bases for generalized spline modules on arbitrary graphs

Creative Commons License

Altınok Bhupal S., Sarıoǧlan S.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.20, no.10, 2021 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 10
  • Publication Date: 2021
  • Doi Number: 10.1142/s0219498821501802
  • Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Generalized splines, algebraic graph theory
  • Hacettepe University Affiliated: Yes

Abstract

Let R be a commutative ring with identity. An edge labeled graph is a graph with edges labeled by ideals of R. A generalized spline over an edge labeled graph is a vertex labeling by elements of R, such that the labels of any two adjacent vertices agree modulo the label associated to the edge connecting them. The set of generalized splines forms a subring and module over R. Such a module is called a generalized spline module. We show the existence of a flow-up basis for the generalized spline module on an edge labeled graph over a principal ideal domain by using a new method based on trails of the graph. We also give an algorithm to determine flow-up bases on arbitrary ordered cycles over any principal ideal domain.