Date of Final Oral Examination (Defense)
Type of Culminating Activity
Master of Science in Mathematics
Jens Harlander, Ph.D.
Zachariah Teitler, Ph.D.
Uwe Kaiser, Ph.D.
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.
Schott, Sarah, "Exploring the Beginnings of Algebraic K-Theory" (2021). Boise State University Theses and Dissertations. 1798.