Tensor Product of C-Injective Modules

2015/03/18 by Mohammad Rahmani, Rahmani, Mohammad, A. J. Taherizadeh +2
Mathematics · #13C05 (Primary) #13D05 (Secondary) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #msc:13C05 #msc:13D05

paper · pdf · doi:10.48550/arxiv.1503.05492

13 pages, to appear in Communications in Algebra

openalex publication_date 2015/03/18 · arxiv created 2016/08/26 · arxiv updated 2016/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R be a Noetherian ring and let C be a semidualizing R-module. In this paper, we are concerned with the tensor and torsion product of C-injective modules. Firstly, it is shown that the tensor product of any two C-injective R-modules is C-injective if and only if the injective hull of C is C-flat. Secondly, it is proved that C is a pointwise dualizing R-module if and only if Tor^R_i(M,N) is C-injective for all C-injective R-modules M and N, and all i ≥ 0. These results recover the celebrated theorems of Enochs and Jenda \citeEJ2.

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