Jürgen Herzog: Rings of Teter type

Abstract

A 0-dimensional local ring \((R,m_R)\) is called a Teter ring, if there exists a local Gorenstein ring \((G,m_G)\) such that R is isomorphic to \(G/(0:m_G)\). This class of rings has been introduced 1974 by William Teter. It has been shown by Huneke and others that a local ring R is a Teter ring if and only if there exists an epimorphism \(\varphi:\omega_R\to m_R\). Here \(\omega_R\) denotes the canonical module of R. The ring is called of Teter type, if there exists a surjective homomorphism from \(\omega_R\) onto the trace of \(\omega_R\). Various classes of algebras of Teter type will be considered.

This is joint work with Oleksandra Gasanova, Takayuki Hibi and Somayeh Moradi.