Lower Algebraic K-Theory of Rings
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This thesis is a first step towards a controlled algebraic K-theory. We give explicit formulas for the proof of Fundamental Theorem of Algebraic K-Theory. As a consequence, we provide explicit estimates on the control of propagation. The first part of this thesis is an introduction to K0 and K1-groups of rings, where we develop necessary background materials. In the second part of this thesis, we prove the Fundamental Theorem of Algebraic K-Theory by elementary means and give explicit formulas. A detailed discussion of propagation control is given at the end of this part. In the last part of this thesis, we introduce negative algebraic K-theory and prove its Fundamental Theorem of Algebraic K-Theory. This work is intended as a first step towards quantitative computations for lower algebraic K-theory.
Subjectcontrolled algebraic K-theory
Zhu, Qinfeng (2018). Lower Algebraic K-Theory of Rings. Master's thesis, Texas A & M University. Available electronically from