摘要翻译:
设f和g是任意域K上的非常多项式。本文研究了多项式环K[f]和K[g]的交集,特别是这个交集是否大于K。当K的特征为零时,我们完全解决了这个问题,并在正特征中给出了各种结果、例子和算法。
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英文标题:
《Polynomials with a common composite》
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作者:
Robert M. Beals, Joseph L. Wetherell and Michael E. Zieve
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最新提交年份:
2008
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分类信息:
一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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一级分类:Mathematics 数学
二级分类:Number Theory 数论
分类描述:Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数,丢番图方程,解析数论,代数数论,算术几何,伽罗瓦理论
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英文摘要:
Let f and g be nonconstant polynomials over an arbitrary field K. In this paper we study the intersection of the polynomial rings K[f] and K[g], and in particular we ask whether this intersection is larger than K. We completely resolve this question when K has characteristic zero, and in positive characteristic we present various results, examples, and algorithms.
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PDF链接:
https://arxiv.org/pdf/0707.1552