Summary: In this paper we introduce the 2-typical de Rham-Witt complex for arbitrary commutative, unital rings and log-rings. We describe this complex for the rings $\Z$ and $\Z_{(2)}$, for the log-ring $(\Z_{(2)},M)$ with the canonical log-structure, and we describe its behaviour under polynomial extensions. In an appendix we also describe the $p$-typical de Rham-Witt complex of $(\Z_{(p)},M)$ for $p$ odd.

13K05, 19D55

de Rham-Witt, topological cyclic homology, algebraic K-theory