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** Krull's principal ideal theorem
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** and Krull's
** Krull's intersection theorem
** Krull's theorem
** and principal
** The Secretariat, the principal administrative mechanism of the CPC, headed by the General Secretary of the Central Committee ;
** Victoria Coach Station, which owns and operates London's principal terminal for long distance bus and coach services.
** Chrysippus, Greek philosopher from Soloi who was the principal systematiser of stoic philosophy ( b. c. 280 BC )
** accessory, for secondary buds formed besides a principal bud ( axillary or terminal );
** Some books, films, video games, and TV shows have one or more eponymous principal characters: Robinson Crusoe, Moll Flanders, Emma, the Harry Potter series, The Legend of Zelda series, I Love Lucy, for example.
** Principal ideal domain, an integral domain in which every ideal is principal
** Bézout domain, an integral domain in which the sum of two principal ideals is again a principal ideal
** Monopole ( mathematics ), a connection over a principal bundle G with a section ( the Higgs field ) of the associated adjoint bundle
** As discussed by economists as the principal – agent problem, agent means anyone supposed to act in the interests of the principal, especially insofar as the actions of the agent cannot be completely monitored by the principal.
** Saint Clair County is the principal county in the The Blue Water Area, a subregion of the Thumb.
** Port Huron is the principal city of the Blue Water Area, a subregion of the Thumb.
** Great Western Main Line, a principal passenger and freight rail route
** The WJ Scott Library, named for a former principal of the College and formerly the College's library, is located in the Karori Campus of the University.
** The compound Galin Khanum – literally, " lady bride " – was the title accorded to the principal noble wife of a Qajar
** Italian: list of principal irregular second and third conjugation verbs
** Reading railway station, a principal railway station serving Reading, Berkshire
** The principal authority for Louvois's life and times is Camille Rousset's Histoire de Louvois ( Paris, 1872 ), a great work founded on the 900 volumes of his despatches at the Depôt de la Guerre.
** Tandya Mahabrahmana or Panchavimsha Brahmana () ( PB ) is the principal Brahmana of both the Kauthuma and Ranayaniya shakhas.
** Jaiminiya Brahmana ( JB ) is the principal Brahmana of the Jaiminiya shakha, divided into three kandas ( sections ).
** Macquarie Street, one of the principal streets of downtown Sydney, home of the New South Wales Parliament
** Macquarie Street, one of the principal streets of Hobart
** Macquarie Street, one of the principal streets of the historic town of Evandale, a town he founded in 1811
** and ideal
** Every unital ring other than the trivial ring contains a maximal ideal.
** If S is a set of sentences of first-order logic and B is a consistent subset of S, then B is included in a set that is maximal among consistent subsets of S. The special case where S is the set of all first-order sentences in a given signature is weaker, equivalent to the Boolean prime ideal theorem ; see the section " Weaker forms " below.
** Stone's representation theorem for Boolean algebras needs the Boolean prime ideal theorem.
** for his fundamental and broad contributions to discrete optimization including his deep research on balanced and ideal matrices, perfect graphs and cutting planes for mixed-integer optimization.
** Dedekind domain, an integral domain in which every nonzero proper ideal factors into a product of prime ideals
** Differential nonlinearity ( DNL ) shows how much two adjacent code analog values deviate from the ideal 1 LSB step.
** Integral nonlinearity ( INL ) shows how much the DAC transfer characteristic deviates from an ideal one.
** France, at least in the early stages of the French Revolution, was the ideal European nation.
** Chili pepper water: Used primarily in Hawaii, this concoction is ideal for cooking.
** Welcome of emigrants by diaspora Jewish community is seen as a possible betrayal of the Zionist ideal — immigration to Israel — and endangerment of Israel's success in retaining and growing its Jewish population.
** New Order ( Mandalorian ), Cassus Fett's ideal of the Mandalorian Neo-Crusaders during the Mandalorian Wars
** In The Moon Is a Harsh Mistress, Robert A. Heinlein presents a human society on the Moon as an ideal anarchy, populated by political exiles and held together by the need for cooperation to ensure mutual survival, coupled with the ease for revenge in the event of harm.
** Citizen journalism forums obeying stricter rules to ensure equal power relationships than is typically the case in blogs, strictly designed to balance libel and free speech laws for a local jurisdiction ( following laws strictly is part of the open politics ideal ).
** and theorem
** Well-ordering theorem: Every set can be well-ordered.
** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.
** König's theorem: Colloquially, the sum of a sequence of cardinals is strictly less than the product of a sequence of larger cardinals.
** Tychonoff's theorem stating that every product of compact topological spaces is compact.
** The Vitali theorem on the existence of non-measurable sets which states that there is a subset of the real numbers that is not Lebesgue measurable.
** The Nielsen – Schreier theorem, that every subgroup of a free group is free.
** The Hahn – Banach theorem in functional analysis, allowing the extension of linear functionals
** The theorem that every Hilbert space has an orthonormal basis.
** The Banach – Alaoglu theorem about compactness of sets of functionals.
** The Baire category theorem about complete metric spaces, and its consequences, such as the open mapping theorem and the closed graph theorem.
** Gödel's completeness theorem for first-order logic: every consistent set of first-order sentences has a completion.
** The numbers and are not algebraic numbers ( see the Lindemann – Weierstrass theorem ); hence they are transcendental.
** Hilbert's basis theorem
** Bayes ' theorem
** More generally, Rademacher's theorem extends the differentiability result to Lipschitz mappings between Euclidean spaces: a Lipschitz map ƒ: U → R < sup > m </ sup >, where U is an open set in R < sup > n </ sup >, is almost everywhere differentiable.
** Lyapunov's central limit theorem
** Superposition theorem, in electronics
** " Kelvin's vorticity theorem for incompressible or barotropic flow ".
** Artin reciprocity law, a general theorem in number theory that provided a partial solution to Hilbert's ninth problem
** Various proofs of the four colour theorem.
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