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Let $p$ be an odd prime and $R$ a $p$-torsion-free commutative$\mathbb{Z}_{(p)}$-algebra. We compute the periodic cyclic homology over $R$ ofthe universal differential graded algebra $R//p$ which is obtained from $R$ byuniversally killing $p$. We furthermore compute the cyclic and negative cyclichomologies of $R//p$ over $R$ in infinitely many degrees.

On the cyclic homology of certain universal differential graded algebras