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 elementsx, y satisfy
where |x | and |y | denote the degrees of x and y.
Beck, Kristen A.; Sather-Wagstaff, Keri Ann (2013-07-01). "A somewhat gentle introduction to differential graded commutative algebra". arXiv:1307.0369 [math.AC].
graded, commutative, ring, algebra, graded, commutative, ring, also, called, skew, commutative, ring, graded, ring, that, commutative, graded, sense, that, homogeneous, elements, satisfy, displaystyle, where, denote, degrees, commutative, graded, ring, with, t. 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 x y 1 x y y x displaystyle xy 1 x y yx 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 editDavid 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 See also editDG algebra graded symmetric algebra alternating algebra supercommutative algebra nbsp This abstract algebra related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Graded commutative ring amp oldid 1179243252, wikipedia, wiki, book, books, library,
