Work

On embeddings of rings into their canonical modules

Year: 2026

Type: preprint

Abstract: We study embeddings of Cohen--Macaulay local rings into their canonical modules such that the quotient of the cokernel by a regular sequence has the residue field as a direct summand. Motivated by almost Gorenstein rings, we prove an Ext-vanishing criterion for finite projective dimension, which implies G-regularity and the generalized Auslander--Reiten condition. We characterize this summand condition for one-dimensional fiber products and numerical semigroup rings. For Stanley--Reisner rings of graphs, we characterize the corresponding condition for graded embeddings in terms of the graph and show that it is equivalent to a strict multiplicity inequality.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.34395

Authors: An, Tran Nguyen, Kumashiro, Shinya, Samanta, Mouma

Institutions: Thai Nguyen University Of Education, Indian Institute of Technology Kharagpur, Osaka Institute of Technology

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Japan Society for the Promotion of Science

OpenAlex ID: W7214724193

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