Semidualizing Modules over Numerical Semigroup Rings
Commutative Algebra
2023-06-28 v1 Group Theory
Abstract
A semidualizing module is a generalization of Grothendieck's dualizing module. For a local Cohen-Macaulay ring , the ring itself and its canonical module are always realized as (trivial) semidualizing modules. Reasonably, one might ponder the question; when do nontrivial examples exist? In this paper, we study this question in the realm of numerical semigroup rings and completely classify which of these rings with multiplicity at most 9 possess a nontrivial semidualizing module. Using this classification, we construct numerical semigroup rings in any multiplicity at least 9 possesses a nontrivial semidualizing module.
Cite
@article{arxiv.2306.14989,
title = {Semidualizing Modules over Numerical Semigroup Rings},
author = {Ela Celikbas and Hugh Geller and Toshinori Kobayashi},
journal= {arXiv preprint arXiv:2306.14989},
year = {2023}
}
Comments
22 pages, comments welcome