Ulrich ideals in the ring $k[[t^5,t^{11}]]$

TL;DR

This paper classifies Ulrich ideals in specific semigroup rings by describing their generators, enhancing understanding of their algebraic structure in these particular cases.

Contribution

It provides a complete description of Ulrich ideals in the rings $k[[t^5,t^{11}]]$ and $k[[t^5,t^6,t^9]]$, including normal forms of their generators.

Findings

Ulrich ideals in $k[[t^5,t^{11}]]$ are explicitly characterized.

Ulrich ideals in $k[[t^5,t^6,t^9]]$ are explicitly characterized.

Normal forms of generators for these ideals are established.

Abstract

The Ulrich ideals in the semigroup rings $k[[t^5, t^{11}]]$ and $k[[t^5,t^6,t^9]]$ are determined, by describing the normal forms of systems of generators, where $k[[t]]$ denotes the formal power series ring over a field $k$.