Sagbi bases over the product of rings

Year 2025, Volume: 38 Issue: 38, 1 - 11, 14.07.2025

Nazia Jabeen , Junaid Khan

https://doi.org/10.24330/ieja.1575706

Abstract

Let $R$ be a commutative ring such that $R=R_1\times \cdots \times R_n$. In this paper, we give a method to compute (strong) Sagbi bases for subalgebras of a polynomial ring over $R$ provided that these bases are computable in a polynomial ring over $R_i$ for $1\leq i \leq n$. As an application, we prove the existence of strong Sagbi bases for subalgebras in a polynomial ring over a principal ideal ring.

Keywords

Gröbner basis , strong Gröbner basis , Sagbi basis , PIR , PID

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