Definition 2

Tag 05XZ, permanent. Cite it as [Bourbaki, Tag 05XZ].

Algebra, chapter II, § 11. Graded modules and rings

Given a ring $A$ and a graduation $(A_\lambda)$ of type $\Delta$ on the additive group $A$ , this graduation is said to be compatible with the ring structure on $A$ if

A_\lambda A_\mu \subset A_{\lambda + \mu} \quad \text{for all } \lambda, \mu \text{ in } \Delta.

The ring $A$ with this graduation is then called a graded ring of type $\Delta$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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