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  2. Wedderburn–Artin theorem - Wikipedia

    en.wikipedia.org/wiki/Wedderburn–Artin_theorem

    In algebra, the Wedderburn–Artin theorem is a classification theorem for semisimple rings and semisimple algebras.The theorem states that an (Artinian) [a] semisimple ring R is isomorphic to a product of finitely many n i-by-n i matrix rings over division rings D i, for some integers n i, both of which are uniquely determined up to permutation of the index i.

  3. Decomposition of a module - Wikipedia

    en.wikipedia.org/wiki/Decomposition_of_a_module

    In abstract algebra, a decomposition of a module is a way to write a module as a direct sum of modules.A type of a decomposition is often used to define or characterize modules: for example, a semisimple module is a module that has a decomposition into simple modules.

  4. Carry (arithmetic) - Wikipedia

    en.wikipedia.org/wiki/Carry_(arithmetic)

    Kummer's theorem states that the number of carries involved in adding two numbers in base is equal to the exponent of the highest power of dividing a certain binomial coefficient. When several random numbers of many digits are added, the statistics of the carry digits bears an unexpected connection with Eulerian numbers and the statistics of ...

  5. Polynomial decomposition - Wikipedia

    en.wikipedia.org/wiki/Polynomial_decomposition

    Algorithms are known for decomposing univariate polynomials in polynomial time. Polynomials which are decomposable in this way are composite polynomials ; those which are not are indecomposable polynomials or sometimes prime polynomials [ 1 ] (not to be confused with irreducible polynomials , which cannot be factored into products of polynomials ).

  6. Arithmetic - Wikipedia

    en.wikipedia.org/wiki/Arithmetic

    Analytic number theory, by contrast, relies on techniques from analysis and calculus. It examines problems like how prime numbers are distributed and the claim that every even number is a sum of two prime numbers. [83] Algebraic number theory employs algebraic structures to analyze the properties of and relations between numbers.

  7. How Trump Got Away With It, According to Jack Smith - AOL

    www.aol.com/trump-got-away-according-jack...

    President-elect Donald Trump speaks to members of the media following a meeting at the US Capitol on Jan. 8, 2025 in Washington, DC. Credit - Valerie Plesch—Bloomberg via Getty Images

  8. New gun laws rolling out in multiple states on Jan. 1, 2025 ...

    www.aol.com/gun-laws-rolling-multiple-states...

    California gun safety regulations going into effect Jan. 1. In September, California Gov. Gavin Newsom signed a series of laws aimed at strengthening gun safety regulations.Those include requiring ...

  9. Function composition - Wikipedia

    en.wikipedia.org/wiki/Function_composition

    If an airplane's altitude at time t is a(t), and the air pressure at altitude x is p(x), then (p ∘ a)(t) is the pressure around the plane at time t. Function defined on finite sets which change the order of their elements such as permutations can be composed on the same set, this being composition of permutations.

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