In mathematics, algebraic K-theory is an important part of homological algebra concerned with defining and applying a sequence of functors from rings to abelian groups, for all integers n. For historical reasons, the lower K-groups K0 and K1 are thought of in somewhat different terms from the higher algebraic K-groups Kn for n ? 2. Indeed, the lower groups are more accessible, and have more applications, than the higher groups. The theory of the higher K-groups is noticeably deeper, and certainly much harder to compute (even when R is the ring of integers).

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