2014/12/08 by Aaron J. Feickert, Feickert, Aaron J., Sean Sather-Wagstaff +1
Mathematics · #13C05 #13C12 #13C13 #13D07 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1412.2654
openalex publication_date 2014/12/08 · openalex created_date 2022/08/22 · openalex updated_date 2026/07/28
Over a noetherian ring, it is a classic result of Matlis that injective\nmodules admit direct sum decompositions into injective hulls of quotients by\nprime ideals. We show that over a Cohen-Macaulay ring admitting a dualizing\nmodule, Gorenstein injective modules admit similar filtrations. We also\ninvestigate Tor-modules of Gorenstein injective modules over such rings. This\nextends work of Enochs and Huang over Gorenstein rings.\n Furthermore, we give examples showing the following: (1) the class of\nGorenstein injective R-modules need not be closed under tensor products, even\nwhen R is local and artinian; (2) the class of Gorenstein injective\nR-modules need not be closed under torsion products, even when R is a\nlocal, complete hypersurface; and (3) the filtrations given in our main theorem\ndo not yield direct sum decompositions, even when R is a local, complete\nhypersurface.\n