Strongly Gorenstein-projective modules over rings of Morita contexts (Q6547692)

Strongly Gorenstein-projective modules, introduced by \textit{D. Bennis} and \textit{N. Mahdou} [J. Pure Appl. Algebra 210, No. 2, 437--445 (2007; Zbl 1118.13014)], build upon the foundational works of Auslander-Bridger and Enochs-Jenda. A module is Gorenstein-projective if and only if it is a direct summand of a strongly Gorenstein-projective module. \textit{N. Gao} and \textit{P. Zhang} [Commun. Algebra 37, No. 12, 4259--4268 (2009; Zbl 1220.16013)] classified all finitely generated strongly Gorenstein-projective modules over upper triangular matrix Artin algebras. Furthermore, \textit{L. Mao} [Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 63(111), No. 3, 271--285 (2020; Zbl 1513.16013)] provided explicit descriptions of the structures of strongly Gorenstein-projective, injective, and flat modules over formal triangular matrix rings.\N\NMeanwhile, Morita rings, introduced by Bass, offer intriguing families of examples. \textit{N. Gao} and \textit{C. Psaroudakis} [Algebr. Represent. Theory 20, No. 2, 487--529 (2017; Zbl 1382.16008)] constructed Gorenstein-projective modules over Morita rings, while \textit{E. L. Green} and \textit{C. Psaroudakis} [Algebr. Represent. Theory 17, No. 5, 1485--1525 (2014; Zbl 1317.16003)] characterized all Gorenstein-projective modules for a specific Morita ring. Building on this foundation, the authors extend the results by describing strongly Gorenstein-projective modules over specific Morita rings, thereby generalizing the theory of strongly Gorenstein-projective modules over formal triangular matrix rings.