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https://en.wikipedia.org/wiki/Double_centralizer_theorem
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https://en.wikipedia.org/wiki/Up_to
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https://en.wikipedia.org/wiki/Ideal_norm
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https://en.wikipedia.org/wiki/Conjugate_diameters
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https://en.wikipedia.org/wiki/Wedderburn%E2%80%93Artin_theorem
If R is a finite-dimensional semisimple k-algebra, then each Di in the above statement is a finite-dimensional division algebra over k
https://en.wikipedia.org/wiki/Invariant_basis_number
Assuming the ultrafilter lemma (a strictly weaker form of the axiom of choice), this result is actually equivalent to the definition given here, and can be taken as an alternative definition
https://en.wikipedia.org/wiki/Grammatical_gender
In linguistics, a grammatical gender system is a specific form of a noun class system, where nouns are assigned to gender categories that are often not related to the real-world qualities of the entities denoted by those nouns
https://en.wikipedia.org/wiki/Outline_of_category_theory
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https://en.wikipedia.org/wiki/Krull's_theorem
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https://en.wikipedia.org/wiki/List_of_differential_geometry_topics
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https://en.wikipedia.org/wiki/Bali_myna
[1]
In 2018, there were three locations on Bali where the birds existed in the wild: the West Bali National Park; Bali's small island of Nusa Penida and Begawan Foundation's breeding and release site at Melinggih Kelod, Payangan
https://en.wikipedia.org/wiki/Theorem
[1]
In mathematics and formal logic, a theorem is a statement that has been proven, or can be proven
https://en.wikipedia.org/wiki/Lithium%E2%80%93sulfur_battery
These constraints are interdependent: increasing sulfur loading or lowering E/S improves projected energy density, but can also increase polarization and lower reversible capacity if ion/electron transport and interfacial stability are not maintained
https://en.wikipedia.org/wiki/Inference_rule
If an argument with true premises follows a rule of inference then the conclusion cannot be false
https://en.wikipedia.org/wiki/Saul_Kripke
|edition=Fall 2016 |language=en}}</ref> [[direct reference theory]], criticism of the [[Frege–Russell view]])<br />[[Admissible ordinal]]<br />[[Kripke structure]]<br />[[Rigid designator|Rigid]] vs
https://en.wikipedia.org/wiki/Markov_chain
Markov chains have many applications as statistical models of real-world processes
https://en.wikipedia.org/wiki/Tragedy_of_the_commons
He postulated that if a herder put more than his allotted number of cattle on the common, overgrazing could result
https://en.wikipedia.org/wiki/Nakayama's_lemma
Informally, Nakayama's lemma says that one can still regard a coherent sheaf as coming from a vector bundle in some sense
https://en.wikipedia.org/wiki/Euclidean_division
This can be confirmed using multiplication, the inverse of division: if each of the 4 people received 2 slices, then 4 × 2 = 8 slices were given out in total
https://en.wikipedia.org/wiki/List_of_general_topology_topics
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https://en.wikipedia.org/wiki/Boolean_prime_ideal_theorem
that ideals in a Boolean algebra can be extended to prime ideals
https://en.wikipedia.org/wiki/List_of_set_theory_topics
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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/Stochastic_calculus
This field was created and started by the Japanese mathematician Kiyosi Itô during World War II
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_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/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/Integral_extension
over a subring A of B if b is a root of some monic polynomial over A