• A graded module that is also a graded ring is called a graded algebra. A graded ring could also be viewed as a graded ⁠ Z {\displaystyle \mathbb {Z} }...
    16 KB (2,819 words) - 14:00, 30 September 2024
  • In mathematics, the associated graded ring of a ring R with respect to a proper ideal I is the graded ring: gr I ⁡ R = ⨁ n = 0 ∞ I n / I n + 1 {\displaystyle...
    5 KB (982 words) - 03:35, 10 May 2024
  • 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...
    1 KB (177 words) - 21:07, 8 October 2023
  • after finitely many steps. Graded A graded module is a module with a decomposition as a direct sum M = ⨁x Mx over a graded ring R = ⨁x Rx such that RxMy...
    22 KB (2,967 words) - 22:27, 6 October 2024
  • cohomology of a cdga is a graded-commutative ring, sometimes referred to as the cohomology ring. A broad range examples of graded rings arises in this way....
    41 KB (5,655 words) - 15:25, 12 December 2023
  • mathematics, the pluricanonical ring of an algebraic variety V (which is nonsingular), or of a complex manifold, is the graded ring R ( V , K ) = R ( V , K V...
    4 KB (464 words) - 18:26, 21 May 2023
  • polynomials, graded rings, have been introduced for generalizing some properties of polynomial rings. A closely related notion is that of the ring of polynomial...
    52 KB (8,219 words) - 13:20, 7 October 2024
  • H^{*}(X,\mathbb {Z} )=\bigoplus _{i=0}^{\infty }H^{i}(X,\mathbb {Z} ),} a graded ring. There are also homology groups H i ( X , Z ) {\displaystyle H_{i}(X...
    99 KB (13,632 words) - 22:52, 9 October 2024
  • into a ring. In fact, it is naturally an N-graded ring with the nonnegative integer k serving as the degree. The cup product respects this grading. The...
    3 KB (589 words) - 00:21, 28 September 2024
  • distributive) graded commutative product operation in cohomology, turning the cohomology of a space X into a graded ring, H∗(X), called the cohomology ring. The...
    8 KB (1,292 words) - 02:10, 28 September 2024