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PreprintarXiv licencearXiv

A Gordon--Green-type result for Gorenstein-projective modules

  • A. M. Bouhada
  • M. Laaraj
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Abstract

Let Λ be a Z-graded Artin algebra which is Iwanaga--Gorenstein. We prove that Λ is CM-finite if and only if the category of gradable Gorenstein-projective modules has finite type, and if and only if the lengths of the indecomposable gradable Gorenstein-projective modules are bounded. Moreover, if Λ is CM-finite, then every Gorenstein-projective Λ-module is gradable. These results provide Gorenstein-projective analogues of the corresponding theorems of Gordon--Green for graded Artin algebras of finite representation type.

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Cite

BibTeXRIS
BibTeX
@misc{bouhada2026gordongreentype,
  title = {{A Gordon--Green-type result for Gorenstein-projective modules}},
  author = {A. M. Bouhada and M. Laaraj},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.17357},
  eprint = {2610.17357},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.17357},
}
RIS
TY  - UNPB
TI  - A Gordon--Green-type result for Gorenstein-projective modules
AU  - A. M. Bouhada
AU  - M. Laaraj
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.17357
UR  - https://arxiv.org/abs/2610.17357
AB  - Let Λ be a Z-graded Artin algebra which is Iwanaga--Gorenstein. We prove that Λ is CM-finite if and only if the category of gradable Gorenstein-projective modules has finite type, and if and only if the lengths of the indecomposable gradable Gorenstein-projective modules are bounded. Moreover, if Λ is CM-finite, then every Gorenstein-projective Λ-module is gradable. These results provide Gorenstein-projective analogues of the corresponding theorems of Gordon--Green for graded Artin algebras of finite representation type.
ER  -