Editing Kernel (algebra) (section)

=== Module homomorphisms ===
Let <math>R</math> be a [[Ring (mathematics)|ring]], and let <math>M</math> and <math>N</math> be <math>R</math>-[[Module (mathematics)|modules]]. If <math>\varphi: M \to N </math> is a module homomorphism, then the kernel is defined to be:<ref name="Dummit Module Kernel Definition">{{harvnb|Dummit|Foote|2004|pp=345–346}}</ref>
: <math> \ker \varphi = \{m \in M \ | \ \varphi (m) = 0\} </math>
Every kernel is a [[submodule]] of the domain module, which means they always contain 0, the additive identity of the module. Kernels of [[abelian group]]s can be considered a particular kind of module kernel when the underlying ring is the [[integer]]s.<ref name="Dummit Module Kernel Definition" />