The Ideal Membership Problem in Non-Commutative Polynomial 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...
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متن کاملThe ideal membership problem and polynomial identity testing
Given a monomial ideal I = 〈m1,m2, · · · ,mk〉 where mi are monomials and a polynomial f as an arithmetic circuit the Ideal Membership Problem is to test if f ∈ I . We study this problem and show the following results. (a) If the ideal I = 〈m1,m2, · · · ,mk〉 for a constant k then there is a randomized polynomial-time membership algorithm to test if f ∈ I . This result holds even for f given by a...
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Let $R$ be a commutative ring with identity and $mathbb{A}(R)$ be the set of ideals of $R$ with non-zero annihilators. In this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $R$, denoted by $mathbb{AG}_P(R)$. It is a (undirected) graph with vertices $mathbb{A}_P(R)=mathbb{A}(R)cap mathbb{P}(R)setminus {(0)}$, where $mathbb{P}(R)$ is...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1996
ISSN: 0747-7171
DOI: 10.1006/jsco.1996.0040