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 |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. In fact, many examples of graded-commutative rings come from algebraic topology and homological algebra.
References
- David Eisenbud, Commutative Algebra. With a view toward algebraic geometry, Graduate Texts in Mathematics, vol 150, Springer-Verlag, New York, 1995. Template:ISBN
- Template:Cite arXiv