Heaps of modules: homological aspects

Abstract

The definitions of projective objects and Gorenstein projective objects in the category of heaps of T-modules are posed, where T is a truss. It is shown that a heap of T-modules P is projective if and only if 𝒢_{e_p}(P) is a projective R(T)-module for all e_p∈ P and a heap of T-modules M is BP Gorenstein projective if and only if 𝒢_{e_m}(M) is a Gorenstein projective R(T)-module for all e_m∈ M. Moreover, we give a functorial description of the BP Gorenstein projective dimension. Finally, it is also proven that a unital truss T is a Gorenstein truss if and only if R(T) is an Iwanaga-Gorenstein ring.

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BibTeX RIS

BibTeX

@misc{wang2026heaps,
  title = {{Heaps of modules: homological aspects}},
  author = {Yongduo Wang and Chenyu Wang and Jian He and Dejun Wu},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2607.18328},
  eprint = {2607.18328},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.18328},
  note = {CC0},
}

RIS

TY  - UNPB
TI  - Heaps of modules: homological aspects
AU  - Yongduo Wang
AU  - Chenyu Wang
AU  - Jian He
AU  - Dejun Wu
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2607.18328
UR  - https://arxiv.org/abs/2607.18328
AB  - The definitions of projective objects and Gorenstein projective objects in the category of heaps of T-modules are posed, where T is a truss. It is shown that a heap of T-modules P is projective if and only if 𝒢_e_p(P) is a projective R(T)-module for all e_p∈ P and a heap of T-modules M is BP Gorenstein projective if and only if 𝒢_e_m(M) is a Gorenstein projective R(T)-module for all e_m∈ M. Moreover, we give a functorial description of the BP Gorenstein projective dimension. Finally, it is also proven that a unital truss T is a Gorenstein truss if and only if R(T) is an Iwanaga-Gorenstein ring.
ER  -

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