Exercise 111.23.1. Suppose that A is a ring and M is an A-module. Let f_ i, i \in I be a collection of elements of A such that
Show that if M_{f_ i} is a finite A_{f_ i}-module, then M is a finite A-module.
Show that if M_{f_ i} is a flat A_{f_ i}-module, then M is a flat A-module. (This is kind of silly if you think about it right.)
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