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algebra > commutative algebra > completion
algebra > abstract algebra > algebraic structure > completion
geometry > topological space > topological algebra > completion
algebra > topological algebra > completion

Terme préférentiel

completion  

Définition(s)

  • In abstract algebra, a completion is any of several related functors on rings and modules that result in complete topological rings and modules. Completion is similar to localization, and together they are among the most basic tools in analysing commutative rings. Complete commutative rings have a simpler structure than general ones, and Hensel's lemma applies to them. In algebraic geometry, a completion of a ring of functions R on a space X concentrates on a formal neighborhood of a point of X: heuristically, this is a neighborhood so small that all Taylor series centered at the point are convergent. An algebraic completion is constructed in a manner analogous to completion of a metric space with Cauchy sequences, and agrees with it in the case when R has a metric given by a non-Archimedean absolute value.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Completion_of_a_ring)

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RDF/XML TURTLE JSON-LD Date de création 21/07/2023, dernière modif. 21/07/2023