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Locally Gorenstein algebras, a generalization of Gorenstein algebras
Abstract
For an Artin algebra Λ, we define the class of locally Gorenstein modules, which is a generalization of semi-Gorenstein projective modules and, therefore, a generalization of projective Gorenstein modules. For a locally Gorenstein module X∈mod Λ we construct underlineχX a subcategory of underlinemod Λ and we prove that the syzygy functor is faithful and full on underlineχX. Using that, we prove that the Igusa-Todorov functions ϕ and ψ vanish on the family of locally Gorenstein modules. Finally, using locally Gorenstein modules, we define the locally Gorenstein algebras, a generalization of Gorenstein algebras, and we prove that their finitistic, and the ϕ and ψ dimensions are finite.
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BibTeX
@misc{alarcon2026locally,
title = {{Locally Gorenstein algebras, a generalization of Gorenstein algebras}},
author = {Leonardo Alarcon and María Andrea Gatica and Marcelo Lanzilotta},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23592},
eprint = {2610.23592},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23592},
}
RIS
TY - UNPB
TI - Locally Gorenstein algebras, a generalization of Gorenstein algebras
AU - Leonardo Alarcon
AU - María Andrea Gatica
AU - Marcelo Lanzilotta
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23592
UR - https://arxiv.org/abs/2610.23592
AB - For an Artin algebra Λ, we define the class of locally Gorenstein modules, which is a generalization of semi-Gorenstein projective modules and, therefore, a generalization of projective Gorenstein modules. For a locally Gorenstein module X∈mod Λ we construct underlineχ_X a subcategory of underlinemod Λ and we prove that the syzygy functor is faithful and full on underlineχ_X. Using that, we prove that the Igusa-Todorov functions ϕ and ψ vanish on the family of locally Gorenstein modules. Finally, using locally Gorenstein modules, we define the locally Gorenstein algebras, a generalization of Gorenstein algebras, and we prove that their finitistic, and the ϕ and ψ dimensions are finite.
ER -