EXPLORING THE BEGINNINGS OF ALGEBRAIC K-THEORY

Author (s) : A.MALARSELVI

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Abstract :
According to K-theory is that part of linear algebra that studies additive or abelian properties (e.g. the determinant). Because linear algebra, and its extensions to linear analysis, is ubiquitous in mathematics, K-theory has turned out to be useful and relevant in most branches of mathematics. Let R be a ring. One defines K(R) as the free abelian group whose basis are the finitely generated projective R-modules with the added relation P ⊕ Q = P + Q. The purpose of this thesis is to study simple settings of the K-theory for rings and to provide a sequence of examples of rings where the associated K-groups K(R) get progressively more complicated. We start with R being a field or a principle ideal domain and end with R being a polynomial.

Keywords : K-theory, Mathematics

Conference Date : 17/09/2021

Pages : 102

Paper ID : IESMDT100