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Freshness: newest result fetched 25 d ago · median age of these results 25 d · 1 of 30 carry a fetch time
https://en.wikipedia.org/wiki/Network_neutrality
[9]
Supporters of net neutrality argue that it prevents ISPs from filtering Internet content without a court order, fosters freedom of speech and democratic participation, promotes competition and innovation, prevents dubious services, and maintains the end-to-end principle, and that users would be intolerant of slow
https://en.wikipedia.org/wiki/British_constitution
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https://en.wikipedia.org/wiki/Intel
com}}"},"footnotes":{"wt":"<ref name=\"xbrlus_1\">{{cite web|url=https://www
https://en.wikipedia.org/wiki/Intel_Corporation
com}}"},"footnotes":{"wt":"<ref name=\"xbrlus_1\">{{cite web|url=https://www
https://en.wikipedia.org/wiki/Nakayama's_lemma
Informally, the lemma immediately gives a precise sense in which finitely generated modules over a commutative ring behave like vector spaces over a field
https://en.wikipedia.org/wiki/Boolean_prime_ideal_theorem
A variation of this statement for filters on sets is known as the ultrafilter lemma
https://en.wikipedia.org/wiki/Outline_of_category_theory
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https://en.wikipedia.org/wiki/List_of_general_topology_topics
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https://en.wikipedia.org/wiki/Krull's_theorem
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https://en.wikipedia.org/wiki/Prime_ideal
This generalizes the following property of prime numbers, known as Euclid's lemma: if p is a prime number and if p divides a product ab of two integers, then p divides a or p divides b
https://en.wikipedia.org/wiki/Basis_(linear_algebra)
: bases) if every element of V can be written in a unique way as a finite linear combination of elements of B
https://en.wikipedia.org/wiki/List_of_set_theory_topics
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https://en.wikipedia.org/wiki/Jerzy_Neyman
[6] Another noted contribution is the Neyman–Pearson lemma, the basis of hypothesis testing
https://en.wikipedia.org/wiki/List_of_representation_theory_topics
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https://en.wikipedia.org/wiki/List_of_topology_topics
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https://en.wikipedia.org/wiki/List_of_commutative_algebra_topics
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https://en.wikipedia.org/wiki/Elliott_H._Lieb
entropy principle]]<br>[[AKLT model|Affleck-Kennedy-Lieb-Tasaki model]]<br>[[Borell–Brascamp–Lieb inequality]]<br>[[Brascamp–Lieb inequality]]<br>[[Brezis–Lieb lemma]]<br>[[Strong subadditivity of quantum entropy#Carlen-Lieb Extension|Carlen–Lieb extension]]<br>[[Temperley–Lieb algebra]]<br>[[Dicke model]
https://en.wikipedia.org/wiki/Integral_extension
over a subring A of B if b is a root of some monic polynomial over A
https://en.wikipedia.org/wiki/Skew-field
In general, if R is a ring and S is a simple module over R, then, by Schur's lemma, the endomorphism ring of S is a division ring;[6] every division ring arises in this fashion from some simple module
https://en.wikipedia.org/wiki/List_of_differential_geometry_topics
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https://en.wikipedia.org/wiki/Stephen_Smale
]]<br>[[Morse–Smale system]]<br>[[Morse–Smale diffeomorphism]]<br>[[Palais–Smale compactness condition]]<br>[[Blum–Shub–Smale machine]]<br>[[Smale–Williams attractor]]<br>[[Morse–Palais lemma]]<br>[[Regular homotopy]]<br>[[Sard's theorem]]<br>[[Sphere eversion]]<br>[[Structural stability]]<br>[[Whitehead
https://en.wikipedia.org/wiki/Noether's_second_theorem
Specifically, the theorem says that if the action has an infinite-dimensional Lie algebra of infinitesimal symmetries parameterized linearly by k arbitrary functions and their derivatives up to order m, then the functional derivatives of L satisfy a system of k differential equations
https://en.wikipedia.org/wiki/Measurable_function
} A function f : X → Y {\displaystyle f:X\to Y} is said to be measurable if for every E ∈ T {\displaystyle E\in \mathrm {T} } the pre-image of E {\displaystyle E} under f {\displaystyle f} is in Σ {\displaystyle \Sigma } ; that is, for all E ∈ T {\displaystyle E\in \mathrm {T} } f − 1 ( E ) := { x ∈ X ∣ f
https://en.wikipedia.org/wiki/Local_ring
1 ≠ 0 and if x is any element of R, then x or 1 − x is a unit
https://en.wikipedia.org/wiki/Faithful_module
For example, if R {\displaystyle R} is a commutative ring and I {\displaystyle I} is an ideal of R {\displaystyle R} , we can consider the quotient ring R / I {\displaystyle R/I} to be an R {\displaystyle R} -module
https://en.wikipedia.org/wiki/Commutator_(ring_theory)
[1]
This element is equal to the group's identity if and only if g and h commute (that is, if and only if gh = hg)
https://en.wikipedia.org/wiki/Ideal_(order_theory)
In this case, the following equivalent definition can be given: a subset I of a lattice ( P , ≤ ) {\displaystyle (P,\leq )} is an ideal if and only if it is a lower set that is closed under finite joins (suprema); that is, it is nonempty and for all x, y in I, the element x ∨ y {\displaystyle x\vee y} of P is also
https://en.wikipedia.org/wiki/Unmixed_ideal
finitely generated) R-module M ≠ 0 {\displaystyle M\neq 0} is a Cohen–Macaulay module if d e p t h ( M ) = d i m ( M ) {\displaystyle \mathrm {depth} (M)=\mathrm {dim} (M)} (in general we have: d e p t h ( M ) ≤ d i m ( M ) {\displaystyle \mathrm {depth} (M)\leq \mathrm {dim} (M)} , see Auslander–Buchsbaum
https://en.wikipedia.org/wiki/Discrete_space
X {\displaystyle X} is defined by letting every superset of the diagonal { ( x , x ) : x ∈ X } {\displaystyle \{(x,x):x\in X\}} in X × X {\displaystyle X\times X} be an entourage, and X {\displaystyle X} is a discrete uniform space if it is equipped with its discrete uniformity
https://en.wikipedia.org/wiki/Projective_dimension
However, every projective module is a free module if the ring is a principal ideal domain such as the integers, or a (multivariate) polynomial ring over a field (this is the Quillen–Suslin theorem)