Ideal membership in signomial rings
نویسندگان
چکیده
منابع مشابه
Ideal Membership in Polynomial Rings over the Integers
We will reproduce a proof, using Hermann’s classical method, in Section 3 below. Note that the computable character of this bound reduces the question of whether f0 ∈ (f1, . . . , fn) for given fj ∈ F [X ] to solving an (enormous) system of linear equations over F . Hence, in this way one obtains a (naive) algorithm for solving the ideal membership problem for F [X ] (provided F is given in som...
متن کاملIdeal Membership Problem
The Ideal Membership Problem is as follows: given f0, f1, . . . , fm ∈ K[x1, . . . , xn], is f0 ∈ 〈f1, . . . , fm〉, where 〈f1, . . . , fm〉 denotes the ideal generated by the fi? An equivalent formulation is: are there q1, . . . , qm ∈ K[x1, . . . , xn] such that f0 = ∑m i=1 qifi? We will solve this question by using Gröbner bases. That is, a Gröbner basis is a “nice” representation of an ideal,...
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Classical Buchberger theory is generalized to a new family of rings. The family includes all subalgebras of the polynomial algebra in one variable. Some subalgebras of polynomial algebras in several variables are included. The new rings are integral domains and have a number of other properties in common with polynomial rings. The rings sit in a field F in appropriate position relative to a val...
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ژورنال
عنوان ژورنال: Publikacije Elektrotehnickog fakulteta - serija: matematika
سال: 2007
ISSN: 0353-8893
DOI: 10.2298/petf0718064m