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...
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Module (mathematics) (redirect from Module over a ring)
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...
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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...
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polynomials, graded rings, have been introduced for generalizing some properties of polynomial rings. A closely related notion is that of the ring of polynomial...
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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...
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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