A counterexample to a conjecture of Ding

TL;DR

This paper provides a counterexample to Ding's conjecture by constructing specific one-dimensional Gorenstein local complete intersections with particular properties, challenging the conjecture's validity.

Contribution

It introduces explicit examples of one-dimensional Gorenstein local complete intersections that disprove Ding's conjecture about the index of such rings.

Findings

Counterexample to Ding's conjecture presented

Examples of one-dimensional local complete intersections with index 5

Generalized Loewy length 6 demonstrated

Abstract

We give a counterexample to a conjecture posed by S. Ding regarding the index of a Gorenstein local ring by exhibiting several examples of one dimensional local complete intersections of embedding dimension three with index 5 and generalized L\"oewy length 6.