2021/08/06 by Ryo Kanda, Kanda, Ryo, Tsutomu Nakamura +1
Mathematics · #13B35 (Secondary) #16D40 #16D70 #16G30 (Primary) #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.AC #math.CT #math.RA #math.RT #msc:13B35 #msc:16D40 #msc:16D70 #msc:16G30
paper · pdf · doi:10.48550/arxiv.2108.03153
44 pages
arxiv created 2021/08/06 · arxiv updated 2021/08/09
For a module-finite algebra over a commutative noetherian ring, we give a complete description of flat cotorsion modules in terms of prime ideals of the algebra, as a generalization of Enochs' result for a commutative noetherian ring. As a consequence, we show that pointwise Matlis duality gives a bijective correspondence between the isoclasses of indecomposable injective left modules and the isoclasses of indecomposable flat cotorsion right modules. This correspondence is an explicit realization of Herzog's homeomorphism induced from elementary duality of Ziegler spectra.