Homomorphism of abelian groups
= Homomorphism of abelian groups
{title2=$f(a+b)=f(a)+f(b)$}
= Abelian group homomorphism
{c}
{synonym}
A <group homomorphism> between <abelian groups>, conventionally written additively. Its <kernel> and <image> are <subgroups>, and the additive formula implies preservation of zero, negation and every integer multiple. Maps on <Mordell-Weil groups> induced by <isogenies of elliptic curves> and by <good reduction> are examples.