i have a question... maybe it is easy and im only doing some mistake.
Given a surjective homomorphism $f\colon \mathbb{Z}^n \rightarrow \mathbb{Z}^m$, then its kernel $K_f$ is isomorphic to $\mathbb{Z}^{n-m}$.
- How can i describe the kernel $K_{\wedge^k f}$ of $\wedge^k f \colon \wedge^k \mathbb{Z}^n \rightarrow \wedge^k \mathbb{Z}^m$ in terms of $K_f$?
- Now, consider an injective morphism $g\colon \mathbb{Z}^n \rightarrow \mathbb{Z}^p$, is the group $\wedge^k \mathbb{Z}^p / \wedge^k g (K_{\wedge^k f})$ isomorphic to some wedge product?
Thanks.