## Defintion ## Given a [[commutative ring]] $R$, a $R$-**geometric algebra** is a [[graded module|graded $R$-module]] and an [[algebra (ring theory)|$R$-algebra]] $A$ with canonical ring homomorphism $i:R \to A$ with an [[isomorphism]] $j:\langle A \rangle_0 \cong R$ and a [[quadratic form]] $(-)^2:\langle A \rangle_1 \to R$. Every $R$-geometric algebra is a $R$-[[Clifford algebra]]. ## See also ## * [[Clifford algebra]] * [[algebra (ring theory)]] * [[real geometric algebra]] * [[graded module]] ## References ## * G. Aragón, J.L. Aragón, M.A. Rodríguez (1997), Clifford Algebras and Geometric Algebra, _Advances in Applied Clifford Algebras_ Vol. 7 No. 2, pg 91–102, doi:10.1007/BF03041220, S2CID:120860757