On Lower Transcendence Degree
On Lower Transcendence Degree
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论较低的超越度
DOI：
10.1006/aima.1998.1749
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发表时间：
1998
影响因子：
1.7
通讯作者：
James J. Zhang
中科院分区：
文献类型：
--
作者：
James J. Zhang
领域的超越程度是一个重要的不变量。非交换代数几何的最新发展表明，我们需要一个类似的除代数不变量，而在它们的中心上不一定是有限的（参见第 9 节）。自 20 世纪 60 年代以来，人们多次尝试定义这样的不变量 [GK、BK、Re1、Re2、Re3、Sc1、Sc2、St]，其中最成功的是 Gelfand 和 Kirillov。在他们的论文 [GK] 中，他们定义了两个不变量，现在分别称为 Gelfand Kirillov 维数 (GKdim) 和 Gelfand Kirillov 超越度 (Tdeg)。对于基域 k 上的代数 A，A 的 GK 维数定义为
The transcendence degree of a field is an important invariant. Recent developments in noncommutative algebraic geometry suggest that we need an analogous invariant for division algebras not necessarily finite over their centers (see Section 9). Since the 1960s several attempts have been made to define such an invariant [GK, BK, Re1, Re2, Re3, Sc1, Sc2, St], the most successful of which is due to Gelfand and Kirillov. In their paper [GK] they defined two invariants, now called Gelfand Kirillov dimension (GKdim) and Gelfand Kirillov transcendence degree (Tdeg) respectively. For an algebra A over a base field k, the GK-dimension of A is defined to be