Homotopy Type Theory filtered algebra > history (changes)

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Definition

< filtered algebra

Given a

category: redirected to nlab
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:

∏ m:ℕ∏ n:ℕ∏ a:ℱ m(A)∏ b:ℱ n(A)[∑ c:ℱ m+n(A)a⋅b=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

Last revised on June 14, 2022 at 21:16:13. See the history of this page for a list of all contributions to it.

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