Isomorphism Theorem - Modules

Modules

The statements of the isomorphism theorems for modules are particularly simple, since it is possible to form a quotient module from any submodule. The isomorphism theorems for vector spaces and abelian groups are special cases of these. For vector spaces, all of these theorems follow from the rank-nullity theorem.

For all of the following theorems, the word “module” will mean “R-module”, where R is some fixed ring.