(projectively coresolved) Gorenstein flat modules over tensor rings

2025/11/18 by Tang, Guoliang, Wei, Jiaqun
Mathematics · #16D90 #18G25 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · doi:10.48550/arxiv.2511.14494

openalex publication_date 2025/11/18 · openalex created_date 2025/11/20 · openalex updated_date 2026/07/28

Abstract

Let T_R(M) be a tensor ring, where R is a ring and M is an N-nilpotent R-bimodule. Under certain conditions, we characterize projectively coresolved Gorenstein flat modules over T_R(M), showing that a T_R(M) module (X,u) is projectively coresolved Gorenstein flat if and only if u is monomorphic and coker(u) is a projectively coresolved Gorenstein flat R-module. A class of Gorenstein at modules over T_R(M) are also explicitly described. We discuss applications to trivial ring extensions and Morita context rings.

Related

• Gorenstein homological modules over tensor rings
• Construction of Gorenstein projective modules over tensor rings
• X-Gorenstein projective and Y-Gorenstein injective modules over tensor rings
• Gorenstein projective, injective and flat modules over trivial ring extensions
• Projectively coresolved Gorenstein flat and Ding projective modules