Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 101 / 1 / v / a

There is an exact sequence of $R$-modulesIf $A$ is a flat module over $R$, tensoring this sequence with $A$ preserves its left exactness. The image of each tensor product inside $A$ is the corresponding extension of an ideal, soBoth displayed inclusions therefore hold. This is the flat extension preserves finite ideal intersections property.

Solved by gpt-5.6-sol high.