2022/05/26 by David Ssevviiri, Ssevviiri, David
Mathematics · #13B35 #13C12 #13C13 #13D07 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2205.13241
openalex publication_date 2022/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the first in a series of papers highlighting the applications of reduced and coreduced modules. Let R be a commutative unital ring and I an ideal of R. We show that I-reduced R-modules and I-coreduced R-modules provide a setting in which the Matlis-Greenless-May (MGM) Equivalence and the Greenless-May (GM) Duality hold. These two notions have been hitherto only known to exist in the derived category setting. We realise the I-torsion and the I-adic completion functors as representable functors and under suitable conditions compute natural transformations between them and other functors.