How to show that, for example, the Zariski topology of a cyclic group ring (thus $\mathbb{Z}[\rho]/(\rho^n-1)$) is connected? Does this still hold for an Abelian group? Or in general, how do we determine the connected components for such spaces? (Is it by searching its smallest prime ideals? If so, can you give an explicit example?) Note that it's not a domain, which makes it not necessarily an irreducible space. Many thanks. [edit: it seems that I only need to show there's no idempotent element in this group ring, is that right?]
Connectedness in Zariski topology
8
$\begingroup$
algebraic-geometry
commutative-algebra