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.)

## Comments (0)