Corollary
Tag 05YA, permanent. Cite it as [Bourbaki, Tag 05YA].
Algebra, chapter II, § 11. Graded modules and rings
Let A, B be two graded rings of type \Delta and u: A \to B a graded homomorphism of graded rings. Then Im(u) is a graded submodule of B, Ker(u) a graded two-sided ideal of A and the bijection A/Ker(u) \to Im(u) canonically associated with u is an isomorphism of graded rings.
It suffices to apply Proposition 3 to u considered as a homomorphism of degree 0 of graded \mathbf{Z}-modules.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
Cited by
Nothing.