摘要翻译:
在以前的一篇论文中,作者和教授一起。Finston博士构造了一类UFDs A_{n,m},其中n,m\in\n^*。这些环对于所有n,m,p,q都是稳定等价的(A_{n,m}[T]\cong A_{p,q}[T]),但只有当(n,m)=(p,q)时,它们才是同构的。这些例子是满足这种行为的特征闭域上的第一个UFD例子。在本文中,我们描述了本文中使用的方法,并表明它们是非常通用的,使读者能够基于相同的原则构造更多这样的示例。
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英文标题:
《On the methods to construct UFD counterexamples to a cancellation
problem》
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作者:
Stefan Maubach
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最新提交年份:
2007
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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:Commutative Algebra 交换代数
分类描述:Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环,模,理想,同调代数,计算方面,不变理论,与代数几何和组合学的联系
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英文摘要:
In a previous paper, the author together with prof. dr. Finston constructed a class of UFDs A_{n,m} where n,m\in \N^*. These rings are all stably equivalent (A_{n,m}[T]\cong A_{p,q}[T] for all n,m,p,q) but are only isomorphic themselves if (n,m)=(p,q). These examples are the first UFD examples over a characteristically closed field satisfying this behavior. In this paper, we describe the methods used in this article, and show that they are very general, enabling the reader to construct many more such examples, based on the same principles.
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PDF链接:
https://arxiv.org/pdf/0706.4226