实对称函数代数的射影自由性
Projective freeness of algebras of real symmetric functions
摘要：
设D^n是C^n中的闭单位多圆盘。考虑D^n上实对称的复值连续函数组成的环C_r，即对D^n中的所有z，f（z）=（f（z^*））^*。证明了C_r是投射自由的，即C_r上的n-生成投射模是自由的.我们还证明了实对称多圆盘代数的几个子代数是射影自由的。
英文摘要：
Let D^n be the closed unit polydisk in C^n. Consider the ring C_r of complex-valued continuous functions on D^n that are real symmetric, that is, f(z)=(f(z^*))^* for all z in D^n. It is shown that C_r is projective free, that is, finitely generated projective modules over C_r are free. We also show that several subalgebras of the real symmetric polydisc algebra are projective free.
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