2005/10/20 by Kamran Divaani-Aazar, Divaani-Aazar, Kamran, Mohammad Ali Esmkhani +3
Mathematics · #13C11 #13H10 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #msc:13C11 #msc:13H10
paper · pdf · doi:10.48550/arxiv.math/0510433
18 pages, to appear in Journal of Algebra
arxiv created 2005/10/20 · openalex publication_date 2005/10/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The structure of cyclically pure injective modules over a commutative ring R is investigated and several characterizations for them are presented. In particular, we prove that a module D is cyclically pure injective if and only if D is isomorphic to a direct summand of a module of the form \HomR(L,E) where L is the direct sum of a family of finitely presented cyclic modules and E is an injective module. Also, we prove that over a quasi-complete Noetherian ring (R,\fm) an R-module D is cyclically pure injective if and only if there is a family \Cλ\λ∈ Λ of cocyclic modules such that D is isomorphic to a direct summand of Πλ∈ ΛCλ. Finally, we show that over a complete local ring every finitely generated module which has small cofinite irreducibles is cyclically pure injective.