Homotopy Type Theory filtered algebra > history (Rev #1)

Definition

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:m:\mathbb{N} and n:n:\mathbb{N}, the product of every mm-multivector and nn-multivector is an m+nm+n-multivector:

m: n: a: m(A) b: n(A)[ c: m+n(A)ab=c]\prod_{m:\mathbb{N}} \prod_{n:\mathbb{N}} \prod_{a:\mathcal{F}_m(A)} \prod_{b:\mathcal{F}_n(A)} \left[\sum_{c:\mathcal{F}_{m+n}(A)} a \cdot b = c\right]

Every geometric $R$-algebra is a filtered RR-algebra.

See also

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