Revision as of 17:42, 18 September 2021 edit EureKB (talk \| contribs) 260 edits clarified ambiguity in the definition Tag: Visual edit ← Previous edit		Revision as of 19:39, 18 September 2021 edit undo EmlynXF (talk \| contribs) 19 edits m Minor edit but crucial. The direct sum is a colimit while the product is a limit, and tensors commute with colimits, not limits. Because of this, the product of flat modules is not necessarily flat, while the sum is. →Localization at primes Next edit →
Line 163: Many local properties are a consequence of the fact that the ring :<math>\~~prod_~~bigoplus_\mathfrak p R_\mathfrak p</math> is a [[faithfully flat module]] when the ~~product~~direct sum is taken over all prime ideals (or over all [[maximal ideal]]s of {{mvar\|R}}). See also [[Faithfully flat descent]]. === Examples of local properties ===

Localization (commutative algebra): Difference between revisions