# zbMATH — the first resource for mathematics

Ideal membership in signomial rings. (English) Zbl 1142.13308
Summary: The paper presents decidability of ideal membership for finitely generated signomial ideals with rational exponents over computable field $$K$$ of characteristic 0. We also prove the existence of nonrecursive ideals in $$K[\bar x^{\mathbb Q}]$$, where $$\bar x^{\mathbb Q}=x_1^{\mathbb Q}\cdots x_n^{\mathbb Q}$$ is a multiplicative copy of the monoid $$\mathbb Q^n=\mathbb Q\times\cdots\times\mathbb Q$$.
##### MSC:
 13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 16S36 Ordinary and skew polynomial rings and semigroup rings 12L05 Decidability and field theory
Full Text: