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  2. Open book decomposition - Wikipedia

    en.wikipedia.org/wiki/Open_book_decomposition

    In mathematics, an open book decomposition (or simply an open book) is a decomposition of a closed oriented 3-manifold M into a union of surfaces (necessarily with boundary) and solid tori. Open books have relevance to contact geometry , with a famous theorem of Emmanuel Giroux (given below) that shows that contact geometry can be studied from ...

  3. Boole's expansion theorem - Wikipedia

    en.wikipedia.org/wiki/Boole's_expansion_theorem

    Boole's expansion theorem, often referred to as the Shannon expansion or decomposition, is the identity: = + ′ ′, where is any Boolean function, is a variable, ′ is the complement of , and and ′ are with the argument set equal to and to respectively.

  4. Decomposition of a module - Wikipedia

    en.wikipedia.org/wiki/Decomposition_of_a_module

    A decomposition with local endomorphism rings [5] (cf. #Azumaya's theorem): a direct sum of modules whose endomorphism rings are local rings (a ring is local if for each element x, either x or 1 − x is a unit). Serial decomposition: a direct sum of uniserial modules (a module is uniserial if the lattice of submodules is a finite chain [6]).

  5. Partial fraction decomposition - Wikipedia

    en.wikipedia.org/wiki/Partial_fraction_decomposition

    In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1]

  6. Lebesgue's decomposition theorem - Wikipedia

    en.wikipedia.org/wiki/Lebesgue's_decomposition...

    In mathematics, more precisely in measure theory, the Lebesgue decomposition theorem [1] provides a way to decompose a measure into two distinct parts based on their relationship with another measure.

  7. Schmidt decomposition - Wikipedia

    en.wikipedia.org/wiki/Schmidt_decomposition

    In linear algebra, the Schmidt decomposition (named after its originator Erhard Schmidt) refers to a particular way of expressing a vector in the tensor product of two inner product spaces. It has numerous applications in quantum information theory , for example in entanglement characterization and in state purification , and plasticity .

  8. Polynomial decomposition - Wikipedia

    en.wikipedia.org/wiki/Polynomial_decomposition

    In mathematics, a polynomial decomposition expresses a polynomial f as the functional composition of polynomials g and h, where g and h have degree greater than 1; it is an algebraic functional decomposition. Algorithms are known for decomposing univariate polynomials in polynomial time.

  9. Primary decomposition - Wikipedia

    en.wikipedia.org/wiki/Primary_decomposition

    The components of a primary decomposition (as well as of the algebraic set decomposition) corresponding to minimal primes are said isolated, and the others are said embedded. For the decomposition of algebraic varieties, only the minimal primes are interesting, but in intersection theory , and, more generally in scheme theory , the complete ...

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