Given a commutative ring RR, a filtered RR-algebra is an $R$-algebra AA whose underlying abelian group is a $\mathbb{N}$-graded $R$-module, such that for natural numbers m:ℕm:\mathbb{N} and n:ℕn:\mathbb{N}, the product of every mm-multivector and nn-multivector is an m+nm+n-multivector:
Every geometric $R$-algebra is a filtered RR-algebra.
graded module
geometric algebra
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