Division algebras of Gelfand-Kirillov transcendence degree 2
Division algebras of Gelfand-Kirillov transcendence degree 2
复制标题
Gelfand-Kirillov 超越度 2 的除代数
DOI：
10.1007/s11856-009-0039-4
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发表时间：
2009
影响因子：
1
通讯作者：
J. Bell
中科院分区：
文献类型：
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作者：
J. Bell
设A是GK维小于3的整环上的n-生成K-代数，Q（A）表示A的商除代数.证明了如果D是Q（A）的GK维至少为2的除子代数，则Q（A）作为左D-向量空间是有限维的。我们利用这一点证明了：如果A是代数闭域K上GK维小于3的G-生成域，则Q（A）的任何除子代数D要么是超越度至多为1的K的G-生成域扩张，要么Q（A）是有限维的左D-向量空间.
Let A be a finitely generated K-algebra that is a domain of GK dimension less than 3, and let Q(A) denote the quotient division algebra of A. We show that if D is a division subalgebra of Q(A) of GK dimension at least 2, then Q(A) is finite dimensional as a left D-vector space. We use this to show that if A is a finitely generated domain of GK dimension less than 3 over an algebraically closed field K, then any division subalgebra D of Q(A) is either a finitely generated field extension of K of transcendence degree at most one, or Q(A) is finite dimensional as a left D-vector space.