Applications of reduced and coreduced modules II: Radicality of the functor Hom_R(R/I, -)

2023/06/22 by Ssevviiri, David
#13D07 #13D30 #16D80 #16S90 #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2306.12871

Abstract

This is the second in a series of papers highlighting the applications of reduced and coreduced modules. Let R be a commutative unital ring and I be an ideal of R. We give necessary and sufficient conditions in terms of I-reduced and I-coreduced R-modules for the functor Hom_R(R/I, -) on the abelian full subcategory of the category of R-modules to be a radical. These conditions further provide a setting for the generalisation of Jans' correspondence, and lead to a new radical class of rings.

Related

• Modules Satisfying the Prime Radical Condition and a Sheaf Construction for Modules I
• Modules (co)reduced relative to another module
• Modules Satisfying the Prime Radical Condition and a Sheaf Construction for Modules II
• Applications of reduced and coreduced modules III: homological properties and coherence of functors
• A Homology Theory for the Semimodules of Radical Submodules