Construction of Gorenstein projective modules over tensor rings

2025/10/24 by Zhao, Guoqiang, Sun, Juxiang
#16D90 #16E05 #16E30 #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2510.21454

Abstract

For a tensor ring T_R(M), we obtain sufficient and necessary conditions to describe all complete projective resolutions and all Gorenstein projective modules. As a consequence, we provide a method for constructing Gorenstein projective modules over T_R(M) from the ones of R. Some applications to trivial ring extensions, Morita context rings and triangular matrix rings are given.

Citations

• Gorenstein homological modules over tensor rings
• Gorenstein projective, injective and flat modules over trivial ring extensions
• Gorenstein projective modules over rings of Morita contexts
• Gorenstein projective modules and recollements over triangular matrix rings
• On Artin algebras arising from Morita contexts
• Stable module theory

Related

• Gorenstein homological modules over tensor rings
• (projectively coresolved) Gorenstein flat modules over tensor rings
• X-Gorenstein projective and Y-Gorenstein injective modules over tensor rings
• Gorenstein projective modules over rings of Morita contexts
• A description of Gorenstein projective modules over the tensor products of algebras