I am having some troubles understanding $k$-affinoid algebras (where ($k$, |.|) is a complete, non Archimedean field, |.| is not trivial) and i am looking for some more concrete and particular examples for better understanding. I was wondering if we can find some $k$-affinoid algebras $(A,||.||)$ where :
- ||.|| is not power multiplicative
- ||.|| is Archimedean.
- $A$ is reduced and ||.|| is not multiplicative.
An example or a construction would really help, thanks