English

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 RR, 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.

Keywords

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

R2 v1 2026-06-28T11:15:00.317Z