函数域中的多元相交多项式OA
Multivariate intersective polynomials in function fields
设Fq是一个含有q个元的有限域,Fq[t]为Fq上的多项式环,研究Fq[t]上的多元多项式的相交性.证明了多元相交多项式h的一些基本性质;利用根序列给出了非常数多元多项式相交性的一个等价条件;另外,引入了与h相关的辅助多项式族,给出了辅助多项式族与差集相关的一种遗传性,进而证明了h的关联因子集为有限集.
Let Fq be the finite field of q elements.Fq[t]is the polynomial ring over Fq.The intersection of multivariate polyno-mials of Fq[t]is studied.Some basic properties of multivariate intersective polynomial h are proved.An equivalent condi-tion for the intersection of non-constant multivariate polynomial is given by using root sequence.The auxiliary polynomial family related to h is introduced,and a kind of heredity related to difference set of the auxiliary polynomial family is given.Furthermore,it is proved that the set of associated factors of h is a finite set.
张慧敏;李晓慧;李国全
天津师范大学数学科学学院,天津 300387天津师范大学数学科学学院,天津 300387天津师范大学数学科学学院,天津 300387
数理科学
有限域上的多项式环相交多项式赋值辅助多项式
polynomial ring over finite fieldintersective polynomialvaluationauxiliary polynomial
《天津师范大学学报（自然科学版）》 2026 (1)
6-10,5
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