Inalgebra, agraded-commutative ring (also called askew-commutative ring) is agraded ring that is commutative in the graded sense; that is,homogeneous elementsx,y satisfy

${\displaystyle xy=(-1{)}^{|x||y|}yx,}$

where |x | and |y | denote the degrees ofx andy.

Acommutative (non-graded) ring, with trivial grading, is a basic example. For a nontrivial example, anexterior algebra is generally not acommutative ring but is agraded-commutative ring.

Acup product oncohomology satisfies the skew-commutative relation; hence, acohomology ring is graded-commutative. In fact, many examples of graded-commutative rings come fromalgebraic topology andhomological algebra.

• David Eisenbud,Commutative Algebra. With a view toward algebraic geometry,Graduate Texts in Mathematics, vol 150,Springer-Verlag, New York, 1995.ISBN 0-387-94268-8
• Beck, Kristen A.;Sather-Wagstaff, Keri Ann (2013-07-01). "A somewhat gentle introduction to differential graded commutative algebra".arXiv:1307.0369 [math.AC].

• DG algebra
• graded-symmetric algebra
• alternating algebra
• supercommutative algebra

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