Higher algebraic $K$-theory of finitely generated torsion modules over principal ideal domains

TL;DR

This paper computes higher algebraic K-theory of Koszul complexes over principal ideal domains and provides comparison techniques for Waldhausen categories lacking the factorization axiom.

Contribution

It introduces methods for calculating higher algebraic K-theory of Koszul complexes over PIDs and offers examples of comparison techniques in Waldhausen categories without the factorization axiom.

Findings

Computed higher algebraic K-theory of Koszul complexes over PIDs.

Provided new comparison techniques for Waldhausen categories.

Illustrated examples demonstrating these techniques.

Abstract

The main purpose of this paper is computing higher algebraic $K$-theory of Koszul complexes over principal ideal domains. The second purpose of this paper is giving examples of comparison techniques on algebraic $K$-theory for Waldhausen categories without the factorization axiom.