Meaning of algebraic K-theory | Babel Free

Definitions

K-theory studied from the point of view of algebra.

uncountable

Equivalents

Examples

“Algebraic cycles are typically studied by imposing one of several equivalence relations. The equivalence relation most relevant for algebraic K-theory is rational equivalence.”

“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⟳.”

“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.”

CEFR level