In commutative algebra, the support of a module M over a commutative ring A is the set of all prime ideals of A such that . It is denoted by . In particular, if and only if its support is empty.
- Let be an exact sequence of A-modules. Then
- If is a sum of submodules , then
- If is a finitely generated A-module, then is the set of all prime ideals containing the annihilator of M. In particular, it is closed.
- If are finitely generated A-modules, then
- If is a finitely generated A-module and I is an ideal of A, then is the set of all prime ideals containing This is .