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Longer titles found: Cantor's intersection theorem (view), Kuratowski's intersection theorem (view)

searching for Intersection theorem 19 found (32 total)

Local ring (2,312 words) [view diff] exact match in snippet view article find links to article

0 } {\displaystyle \bigcap _{i=1}^{\infty }m^{i}=\{0\}} (Krull's intersection theorem), and it follows that R with the m-adic topology is a Hausdorff space

Artin–Rees lemma (1,367 words) [view diff] exact match in snippet view article find links to article

M finitely-generated. One consequence of the lemma is the Krull intersection theorem. The result is also used to prove the exactness property of completion

Noetherian ring (2,773 words) [view diff] exact match in snippet view article find links to article

property (for example, the Lasker–Noether theorem and the Krull intersection theorem). Noetherian rings are named after Emmy Noether, but the importance

Homological conjectures in commutative algebra (1,050 words) [view diff] case mismatch in snippet view article find links to article

resolution, then R {\displaystyle R} is a Cohen–Macaulay ring. The Intersection Theorem. If M ⊗ R N ≠ 0 {\displaystyle M\otimes _{R}N\neq 0} has finite length

Matroid intersection (1,822 words) [view diff] exact match in snippet view article find links to article

graphs and finding arborescences in directed graphs. The matroid intersection theorem, due to Jack Edmonds, says that there is always a simple upper bound

Wolfgang Krull (291 words) [view diff] exact match in snippet view article find links to article

Krull–Azumaya theorem Krull–Schmidt category Krull–Schmidt theorem Krull's intersection theorem Krull's principal ideal theorem Krull's separation lemma Krull's

Ahlswede–Khachatrian theorem (2,051 words) [view diff] exact match in snippet view article find links to article

that no element is contained in all sets of the family. Katona's intersection theorem determines the maximum size of an intersecting family of subsets

Algebraic surface (973 words) [view diff] exact match in snippet view article find links to article

abelian group consisting of all the divisors on S. Then due to the intersection theorem D ( S ) × D ( S ) → Z : ( X , Y ) ↦ X ⋅ Y {\displaystyle {\mathcal

Commutative algebra (2,025 words) [view diff] exact match in snippet view article find links to article

is the case, in particular of Lasker–Noether theorem, the Krull intersection theorem, and Nakayama's lemma. Furthermore, if a ring is Noetherian, then

I-adic topology (651 words) [view diff] exact match in snippet view article find links to article

that case, the 𝔞-adic topology is called separated. By Krull's intersection theorem, if R is a Noetherian ring which is an integral domain or a local

Primary ideal (1,084 words) [view diff] exact match in snippet view article find links to article

m n = 0 {\displaystyle \cap _{n>0}{\mathfrak {m}}^{n}=0} (Krull intersection theorem) where each m n {\displaystyle {\mathfrak {m}}^{n}} is m {\displaystyle

Jack Edmonds (1,543 words) [view diff] exact match in snippet view article find links to article

linear programming to discrete mathematics, he proved the matroid intersection theorem, a very general combinatorial min-max theorem which, in modern terms

Jacobson's conjecture (588 words) [view diff] exact match in snippet view article find links to article

satisfy Jacobson's conjecture. This is a consequence of the Krull intersection theorem. Fully bounded Noetherian rings Noetherian rings with Krull dimension

Completion of a ring (1,582 words) [view diff] exact match in snippet view article find links to article

intersection reduces to the zero element of the ring; by the Krull intersection theorem, this is the case for any commutative Noetherian ring which is an

Stalk (sheaf) (1,588 words) [view diff] exact match in snippet view article

smooth functions at the origin is a non-Noetherian ring. The Krull intersection theorem says that this cannot happen for a Noetherian ring.) On an affine

Germ (mathematics) (2,684 words) [view diff] exact match in snippet view article

derivatives vanish. If this ring were Noetherian, then the Krull intersection theorem would imply that a smooth function whose Taylor series vanished would

Reflexive space (6,409 words) [view diff] no match in snippet view article find links to article

closed bounded convex subsets of X {\displaystyle X} has nonempty intersection. Theorem—A real Banach space is reflexive if and only if every pair of non-empty

Ring (mathematics) (13,738 words) [view diff] exact match in snippet view article

if R is a Noetherian local ring with maximal ideal I, by Krull's intersection theorem. The construction is especially useful when I is a maximal ideal

Erdős–Ko–Rado theorem (5,592 words) [view diff] exact match in snippet view article find links to article

(2020). Ahlswede, Rudolf; Khachatrian, Levon H. (1997), "The complete intersection theorem for systems of finite sets", European Journal of Combinatorics, 18