String algebras over local rings: regular examples

TL;DR

This paper generalizes the concept of string algebras by replacing the ground field with noetherian local rings, providing a method to generate examples over regular local rings depending on their Krull dimension.

Contribution

It introduces a new framework for string algebras over local rings and offers a systematic way to construct examples based on the Krull dimension.

Findings

Generalization of string algebras to noetherian local rings

Method to generate examples over regular local rings

Dependence on Krull dimension for construction

Abstract

String algebras, in the usual sense, are finite-dimensional algebras over a given ground field. We recall a generalisation of the definition of a string algebra, which was introduced in a previous paper of the author. This generalisation replaces the ground field with a noetherian local ring. We provide a way to generate examples of string algebras over any regular local ring, which depends on the Krull dimension.