1. A new class of finitely generated polynomial subalgebras without finite SAGBI bases.
- Author
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Kuroda, Shigeru
- Subjects
- *
GROBNER bases , *RING theory , *POLYNOMIALS , *POLYNOMIAL rings , *FINITE, The , *ALGEBRA , *CHEBYSHEV polynomials - Abstract
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 uncountable, as well as a subalgebra with finitely many distinct initial algebras. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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