  We study certain extensions of the Adler map on Grassmann algebras
$\Gamma(n)$ of order $n$. We consider a known Grassmann-extended Adler map, and
assuming that $n=1$ we obtain a commutative extension of Adler's map in six
dimensions. We show that the map satisfies the Yang--Baxter equation, admits
three invariants and is Liouville integrable. We solve the map explicitly,
viewed as a discrete dynamical system.
