Two-sided coherent algebras over any field with $\mathcal{PGF}(R)\subsetneq\mathcal{GP}(R)$
Year: 2026
Type: preprint
Abstract: For a ring $R$, let $\mathcal{GP}(R)$, $\mathcal{GF}(R)$, and $\mathcal{PGF}(R)$ denote the classes of Gorenstein projective, Gorenstein flat, and projectively coresolved Gorenstein flat left $R$-modules, respectively. We answer negatively the question whether $\mathcal{GP}(R)=\mathcal{PGF}(R)$ 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 $\mathcal{PGF}(T)\subsetneq\mathcal{GP}(T)$.
Source: arXiv (Cornell University)
Author: Zhang, Chencheng
Institution: Shanghai Jiao Tong University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4656525603
OpenAlex ID: W7203921558