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摘要翻译：
在不假定标准有限条件、无以太性或Goldie性质的情况下，我们发展了任意结合代数R的有理理想理论。Amitsur-Martindale商环取代了古典商环，古典商环是理性理想先前定义的基础，但在一般情况下是不可用的。我们的主要结果是关于仿射代数群G在R上的有理作用，在代数闭基域上，我们证明了通有有理理想的一个存在唯一性结果：对于R的每一个G-有理理想I，由I定义的有理谱Rat R的闭子集是Rat R上唯一的G-轨道的闭包。在附加的Goldie假设下，这是由Moeglin和Rentschler（在特征零中）和Vonessen（在任意特征中）建立的，回答了Dixmier的一个问题。
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英文标题：
《Group actions and rational ideals》
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作者：
Martin Lorenz
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最新提交年份：
2009
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分类信息：
一级分类：Mathematics 数学
二级分类：Rings and Algebras 环与代数
分类描述：Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups
非交换环与代数，非结合代数，泛代数与格论，线性代数，半群
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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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英文摘要：
We develop the theory of rational ideals for arbitrary associative algebras R without assuming the standard finiteness conditions, noetherianness or the Goldie property. The Amitsur-Martindale ring of quotients replaces the classical ring of quotients which underlies the previous definition of rational ideals but is not available in a general setting. Our main result concerns rational actions of an affine algebraic group G on R. Working over an algebraically closed base field, we prove an existence and uniqueness result for generic rational ideals: for every G-rational ideal I of R, the closed subset of the rational spectrum Rat R that is defined by I is the closure of a unique G-orbit in Rat R. Under additional Goldie hypotheses, this was established earlier by Moeglin and Rentschler (in characteristic zero) and by Vonessen (in arbitrary characteristic), answering a question of Dixmier.
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PDF链接：
https://arxiv.org/pdf/0801.3472
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