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Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.

2 votes
0 answers
211 views

Open subset in the flat topology on Spec(R)

Let $R$ be a commutative ring and let $S \subset \mathrm{Spec}(R)$ be a subset. Suppose that for each $P \in S$ there exists a Zariski open neighborhood $U$ of $P_P \in \mathrm{Spec}(R_P)$ such that $ …
Georg S.'s user avatar
  • 313
10 votes
5 answers
836 views

What kind of subset is Spec(R_P) in Spec(R)?

While trying to prove some properties of a subset of a prime spectrum I arrived at the following question: Let $R$ be a commutative ring and let $P \in \mathrm{Spec}(R)$. We can consider $\mathrm{Spec …
Georg S.'s user avatar
  • 313