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Projective freeness of algebras of real symmetric functions

Published 4 Mar 2011 in math.KT, math.AC, and math.FA | (1103.0899v3)

Abstract: Let Dn be the closed unit polydisk in Cn. Consider the ring C_r 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 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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