Meanings
- uncountablealgebraic geometryK-theory studied from the point of view of algebra.
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 612 more examples
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 ix2014, 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.
Translations
French K-théorie algébrique
- K-théorie algébriqueK theory studied from the point of view of algebra
German algebraische K-Theorie
- algebraische K-TheorieK theory studied from the point of view of algebra
Cite this entry
algebraic K-theory. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/algebraic%20K-theory
“algebraic K-theory.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/algebraic%20K-theory. Accessed November 5, 2026.
WatkinsX Dictionary, s.v. “algebraic K-theory,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/algebraic%20K-theory.
Source: algebraic K-theory on Wiktionary, CC BY-SA 4.0.