Graded-commutative ring
In algebra, a graded-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 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.
