2025/07/12 by Yongyun Qin, Qin, Yongyun
Mathematics · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Category Theory (math.CT) #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2507.09109
openalex publication_date 2025/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we introduce compatible cleft extensions of abelian categories, and we prove that if (B,A, e,i,l) is a compatible cleft extension, then both the functor l and the left adjoint of i preserve Gorenstein projective objects. Moreover, we give some necessary conditions for an object of A to be Gorenstein projective, and we show that these necessary conditions are also sufficient in some special case. As applications, we unify some known results on the description of Gorenstein projective modules over triangular matrix rings, Morita context rings with zero homomorphisms and θ-extensions.