Publication Date

5-2021

Date of Final Oral Examination (Defense)

3-3-2021

Type of Culminating Activity

Thesis

Degree Title

Master of Science in Mathematics

Department

Mathematics

Supervisory Committee Chair

Jens Harlander, Ph.D.

Supervisory Committee Member

Zachariah Teitler, Ph.D.

Supervisory Committee Member

Uwe Kaiser, Ph.D.

Abstract

According to Atiyah, 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 K0(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 K0(R) get progressively more complicated. We start with R being a field or a principle ideal domain and end with R being a polynomial ring on two variables over a non-commutative division ring.

DOI

10.18122/td.1798.boisestate

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