2021/10/17 by S. Kuroda, Kuroda, Shigeru
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Commutative Algebra (math.AC) #FOS: Mathematics #Formal Methods in Verification #Polynomial and algebraic computation #Primary 13E15 #Secondary 13P10
paper · pdf · doi:10.48550/arxiv.2110.08748
openalex publication_date 2021/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of initial ideal for an ideal of a polynomial ring appears in the theory of Gröbner basis. Similarly to the initial ideals, we can define the initial algebra for a subalgebra of a polynomial ring, or more generally of a Laurent polynomial ring, which is used in the theory of SAGBI (Subalgebra Analogue to Gröbner Bases for Ideals) basis. The initial algebra of a finitely generated subalgebra is not always finitely generated, and no general criterion for finite generation is known. The aim of this paper is to present a new class of finitely generated subalgebras having non-finitely generated initial algebras. The class contains a subalgebra for which the set of initial algebras is continuum, as well as a subalgebra with finitely many distinct initial algebras.