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Words, grammatical forms and meanings linked to the ontology.

algebraic K-theory en · NOUN

Meanings

  1. (uncountable) K-theory studied from the point of view of algebra.
    • Algebraic K-theory has two components: the classical theory which centers around the Grothendieck group K#95;0 of a category and uses explicit algebraic presentations and higher algebraic K-theory which requires topological or homological machinery to define. 2013, Charles A. Weibel, The K-book: An Introduction to Algebraic K-theory, American Mathematical Society, page ix:
    • 2014, Daniel Scott Farley, Ivonne Johanna Ortiz, Algebraic K-theory of Crystallographic Groups, Springer, Lecture Notes in Mathematics 2113, page 1, Algebraic K-theory is a branch of algebra dealing with linear algebra over a general ring R instead of a field. […] Algebraic K-theory plays an important part in many areas of mathematics, especially number theory, algebraic topology and algebraic geometry.
    • Algebraic cycles are typically studied by imposing one of several equivalence relations. The equivalence relation most relevant for algebraic K-theory is rational equivalence. 1999, E. M. Friedlander, “Lecture VII. Beilinson's vision”, in H. Bass, A. O. Kuku, C. Pedrini, editors, Algebraic K-theory And Its Applications, World Scientific, page 61:

Deriveds

higher algebraic K-theory

Relateds

K-group · K-theory · topological K-theory

Translations (2)

de algebraische K-Theorie (K theory studied from the point of view of algebra) · fr K-théorie algébrique (K theory studied from the point of view of algebra)