Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 9 min ago
PreprintarXiv licencearXiv

On End-Semidualizing Modules

  • Luigi Ferraro
  • Justin Lyle
Open at sourcePDFDOICite

Abstract

We introduce and study the notion of End-semidualizing modules which are generalizations of semidualizing modules in the classical sense, and also extend the notion of S−R semidualizing bimodules studied by Holm-White and Wakamatsu. By constrast with these notions, End-semidualizing modules exist abundantly. We characterize these modules by the inclusion of projective and flat modules in their Auslander class, or injective modules in their Bass class, and give criteria for when these Foxby classes satisfy the two-out-of-three property. Over commutative Noetherian rings, we prove base-change and duality results, and characterize local depth inequalities by the inclusion of all modules of finite flat or injective dimension in the corresponding classes.

Related

  1. STRONGLY ϕ-FLAT MODULES, STRONGLY NONNIL-INJECTIVE MODULES AND THEIR HOMOLOGICAL DIMENSIONS
    Xiaolei Zhang, Shiqi Xing, Wei Qi
    Rocky Mountain Journal of MathematicsPeer-reviewedLicence not statedFull text6 citedAlgebra & number theoryOpenAlex
  2. One-periodic category of twisted complexes, Cohen-Macaulay modules and differential modules
    Joseph Winspeare
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Tate modules as condensed modules
    Valerio Melani, Hugo Pourcelot, Gabriele Vezzosi
    Bulletin of the London Mathematical SocietyPeer-reviewedCC BY 4.0Full textAlgebra & number theoryGeometry & topologyHAL
  4. Self-Orthogonal τ-Tilting Modules and Tilting Modules III: Finitistic Dimension
    Xiaojin Zhang, Panyue Zhou
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  5. Self-Orthogonal τ-Tilting Modules and Tilting Modules II: Annihilator Separation
    Xiaojin Zhang
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{ferraro2026endsemidualizing,
  title = {{On End-Semidualizing Modules}},
  author = {Luigi Ferraro and Justin Lyle},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37924},
  eprint = {2610.37924},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37924},
}
RIS
TY  - UNPB
TI  - On End-Semidualizing Modules
AU  - Luigi Ferraro
AU  - Justin Lyle
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37924
UR  - https://arxiv.org/abs/2610.37924
AB  - We introduce and study the notion of End-semidualizing modules which are generalizations of semidualizing modules in the classical sense, and also extend the notion of S−R semidualizing bimodules studied by Holm-White and Wakamatsu. By constrast with these notions, End-semidualizing modules exist abundantly. We characterize these modules by the inclusion of projective and flat modules in their Auslander class, or injective modules in their Bass class, and give criteria for when these Foxby classes satisfy the two-out-of-three property. Over commutative Noetherian rings, we prove base-change and duality results, and characterize local depth inequalities by the inclusion of all modules of finite flat or injective dimension in the corresponding classes.
ER  -