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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
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