# The Structure of Ulrich ideals in hypersurfaces

## TL;DR

This paper characterizes Ulrich ideals in hypersurface rings, constructs their minimal free resolutions, and explores their structure specifically in rings of the form R = k[[X, Y]]/(f).

## Contribution

It provides a new characterization of Ulrich ideals in hypersurfaces and explicitly constructs their minimal free resolutions.

## Key findings

- Ulrich ideals are characterized in hypersurface rings.
- A concrete method to construct minimal free resolutions of Ulrich ideals.
- Ulrich ideals are explored in rings of the form R = k[[X, Y]]/(f).

## Abstract

This paper studies Ulrich ideals in hypersurface rings. A characterization of Ulrich ideals is given. Using the characterization, we construct a minimal free resolution of an Ulrich ideal concretely. We also explore Ulrich ideals in a hypersurface ring of the form R = k[[X, Y]]/(f).