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 P: 449 Well the question I'm referring to is (in the context of lie algebras but similar for linear algebra): 'describe the kernel of the canonical homomorphism $\phi : \mathfrak{g} \to \mathfrak{g} / \mathfrak{h}$' defined by $\phi (x)=x+\mathfrak{h}$ for all $x\in\mathfrak{g}$ where $\mathfrak{g}$ is any lie algebra (vector space with some additional properties) and $\mathfrak{h}$ is an ideal (subspace with some additional properties) of $\mathfrak{g}$. I've found that $\text{Ker}( \phi ) = \mathfrak{h}$ but how would I present a basis? What I mean by finding the kernel is using the definition $\{ v\in V : \phi v)=0 \}$