Zhu, Qinfeng (2018-05). Lower Algebraic K-Theory of Rings. Master's Thesis. Thesis uri icon

abstract

  • 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.
  • 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.

publication date

  • May 2018
  • May 2018