K'-Theory of a Local Ring of Finite Cohen-Macaulay Type

TL;DR

This paper investigates the algebraic K'-theory of a specific class of local rings with finite Cohen-Macaulay type, providing a detailed description via exact sequences involving related rings.

Contribution

It introduces a long exact sequence relating K'-theory of the ring to that of the Auslander algebra and other rings, advancing understanding of their algebraic invariants.

Findings

Describes a long exact sequence involving K'-groups and other rings' K-groups.

Provides explicit calculations for rings of finite Cohen-Macaulay type.

Enhances understanding of the structure of K'-theory in this context.

Abstract

We study the K'-theory of a CM Henselian local ring R of finite Cohen-Macaulay type. We first describe a long exact sequence involving the groups $K_i'(R)$ and the K-groups of certain other rings, including the Auslander algebra. By examining the terms and maps in the sequence, we obtain information about K'(R).