Radical property of the traces of the canonical modules of Cohen-Macaulay rings

TL;DR

This paper introduces a new class of Noetherian rings that interpolates between Gorenstein and Cohen-Macaulay rings, demonstrating its stability under various ring operations and its proximity to Gorenstein rings in specific algebraic structures.

Contribution

It defines a novel ring property bridging Gorenstein and Cohen-Macaulay rings, with proofs of stability under common operations and applications to special algebraic structures.

Findings

New ring property between Gorenstein and Cohen-Macaulay

Stability under localization, polynomial extension, flat extension, tensor, and Segre products

Close relation to Gorenstein property in specific algebraic structures

Abstract

In this paper, we define a new concept of Noetherian commutative rings which stands between Gorenstein and Cohen-Macaulay properties. We show that this new property keep hold under common operations of commutative rings such as localization, polynomial extension and under mild assumptions, flat extension, tensor product, Segre product and so on. We show that for Schubert cycles, the Ehrhart rings of cycle graphs and perfect graphs, this new concept is close to Gorenstein property.