English
The pushforward map on ideals, induced by a ring homomorphism f, is a ring homomorphism from the ring of ideals of R to the ring of ideals of S.
Русский
Пушфорвардное отображение идеалов, индуцированное кольцевым гомоморфизмом f, образует кольцевой гомоморфизм между кольцами идеалов R и S.
LaTeX
$$def mapHom : Ideal R →+* Ideal S where …$$
Lean4
/-- The pushforward `Ideal.map` as a (semi)ring homomorphism. -/
@[simps]
def mapHom : Ideal R →+* Ideal S where
toFun := map f
map_mul' := Ideal.map_mul f
map_one' := by simp only [one_eq_top, Ideal.map_top f]
map_add' I J := Ideal.map_sup f I J
map_zero' := Ideal.map_bot
