Year: 2026
Type: preprint
Abstract: Let $R$ be a ring and $M$ a left $R$-module. We prove that $M$ is an $ω_1$-indexed inverse limit of injective modules with split epimorphic connecting maps, and $M$ is also an $ω$-indexed inverse limit of a stationary tower defined by a split monic endomorphism of one injective module. These constructions answer two questions of Bergman. We then study the class of direct summands of $ω$-indexed inverse limit of injective modules with epimorphic connecting maps. Over a commutative Noetherian ring $R$, they are precisely the Enochs cotorsion modules if and only if $\operatorname{gldim}R\leq1$ and $\operatorname{Spec}R$ is countable.
Source: arXiv (Cornell University)
Author: Zhang, Chencheng
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4656525603
OpenAlex ID: W7214983720