On embeddings of rings into their canonical modules

Tran Nguyen An; Shinya Kumashiro; Mouma Samanta

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arXiv · 2609.34395

On embeddings of rings into their canonical modules

Tran Nguyen An·Shinya Kumashiro·Mouma Samanta

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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.

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Tran Nguyen An, Shinya Kumashiro, Mouma Samanta. 2026-09-28. On embeddings of rings into their canonical modules. https://arxiv.org/abs/2609.34395

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