PreprintCC0arXiv
Two-sided coherent algebras over any field with š¯’«š¯’¢ā„±(R)subsetneqš¯’¢š¯’«(R)
Abstract
For a ring R, let š¯’¢š¯’«(R), š¯’¢ā„±(R), and š¯’«š¯’¢ā„±(R) denote the classes of Gorenstein projective, Gorenstein flat, and projectively coresolved Gorenstein flat left R-modules, respectively. We answer negatively the question whether š¯’¢š¯’«(R)=š¯’«š¯’¢ā„±(R) for every ring. More precisely, over every field k we construct a left and right coherent central k-algebra T and a strongly Gorenstein projective left T-module which is not Gorenstein flat; hence š¯’«š¯’¢ā„±(T)subsetneqš¯’¢š¯’«(T).
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BibTeX
@misc{zhang2026twosided,
title = {{Two-sided coherent algebras over any field with $\mathcalPGF(R)\subsetneq\mathcalGP(R)$}},
author = {Chencheng Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.18722},
eprint = {2608.18722},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.18722},
note = {CC0},
}
RIS
TY - UNPB
TI - Two-sided coherent algebras over any field with š¯’«š¯’¢ā„±(R)subsetneqš¯’¢š¯’«(R)
AU - Chencheng Zhang
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2608.18722
UR - https://arxiv.org/abs/2608.18722
AB - For a ring R, let š¯’¢š¯’«(R), š¯’¢ā„±(R), and š¯’«š¯’¢ā„±(R) denote the classes of Gorenstein projective, Gorenstein flat, and projectively coresolved Gorenstein flat left R-modules, respectively. We answer negatively the question whether š¯’¢š¯’«(R)=š¯’«š¯’¢ā„±(R) for every ring. More precisely, over every field k we construct a left and right coherent central k-algebra T and a strongly Gorenstein projective left T-module which is not Gorenstein flat; hence š¯’«š¯’¢ā„±(T)subsetneqš¯’¢š¯’«(T).
ER -