Type sequences of one-dimensional local analytically irreducible rings

TL;DR

This paper extends the concept of type sequences to a broader class of rings, providing a new invariant to characterize various ring types such as almost Gorenstein and maximal length rings.

Contribution

It introduces a generalized notion of type sequences for non-residually rational rings, enabling new classifications and characterizations.

Findings

Type sequences are extended to non-residually rational rings.

Characterization of almost Gorenstein rings using the new invariant.

Identification of rings of maximal length through the extended type sequence.

Abstract

We extend the notion of type sequence to rings that are not necessarily residually rational. Using this invariant we characterize different types of rings as almost Gorenstein rings and rings of maximal length.