Von Neumann regular group rings not representable as rings of continuous functions (Q1205163)

The authors prove the following theorem: Let \(G\) be an abelian \(p\)-group, \(K\) a field of characteristic \(\neq p\), and suppose that \(K\) does not contain a primitive \(p^ n\)th root of unity for some \(n\geq 1\). Suppose furthermore that \(G\) cannot be written as \(G_ 1\oplus G_ 2\) where \(G_ 1\) is countable and \(G_ 2\) has exponent \(\leq p^{n-1}\). Then \(K[G]\) is not representable as a ring of continuous functions on its spectrum.