  An almost commutative algebra, or a $\rho$-commutative algebra, is an algebra
which is graded by an abelian group and whose commutativity is controlled by a
function called a commutation factor. The same way as a formulation of a
supermanifold as a ringed space, we introduce concepts of the
$\rho$-commutative versions of manifolds, Q-manifolds, Berezin volume forms,
and the modular classes. They are generalizations of the ones in supergeometry.
We give examples including a $\rho$-commutative version of the Schouten bracket
and a noncommutative torus.
