Graded-commutative ring

In algebra, a graded-commutative ring (also called a skew-commutative ring) is a graded ring that is commutative in the graded sense; that is, homogeneous elements "x", "y" satisfy
where , denote the degrees of "x", "y".
A commutative (non-graded) ring, with trivial grading, is a basic example. An exterior algebra is an example of a graded-commutative ring that is not commutative in the non-graded sense.
A cup product on cohomology satisfies the skew-commutative relation; hence, a cohomology ring is graded-commutative. In fact, many examples of graded-commutative rings come from algebraic topology and homological algebra.