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 |x | and |y | denote the degrees of x and y.
A commutative (non-graded) ring, with trivial grading, is a basic example.
For example, an exterior algebra is generally not a commutative ring but is a graded-commutative ring.
A cup product on cohomology satisfies the skew-commutative relation; hence, a cohomology ring is graded-commutative.
This abstract algebra-related article is a stub.