algebraic K-theory en · NOUN
Meanings
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(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
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)