Projective freeness of algebras of real symmetric functions
Abstract
Let Dn be the closed unit polydisk in Cn. Consider the ring Cr of complex-valued continuous functions on Dn that are real symmetric, that is, f(z)=(f(z*))* for all z in Dn. It is shown that Cr is projective free, that is, finitely generated projective modules over Cr are free. We also show that several subalgebras of the real symmetric polydisc algebra are projective free.
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