2014/03/24 by Helmut Zöschinger, Zöschinger, Helmut
Mathematics · #13B35 #13C11 #13J10 #16P70 #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA) #math.AC #math.RA #msc:13B35 #msc:13C11 #msc:13J10 #msc:16P70
paper · pdf · doi:10.48550/arxiv.1403.5957
11 pages, in German
arxiv created 2014/03/24 · arxiv updated 2014/03/25
Let (R,m) be a noetherian local ring and let C be the class of all R-modules M which possess a reflexive submodule U such that M/U is finitely generated. For every R-module M∈ C the canonical embedding φ: M→ Moo is pure-essential. We investigate in the first section under which conditions the reverse is true, for example if R is a discrete valuation ring or if R does not have nilpotent elements and M is flat. In section 2 we determine all reflexive and flat R-modules with the help of a certain analogy between the localization Rq and the injective hull of R/q. In section 3 we show: If the property 'pure-essential' is transitive for a domain R, then it follows that dim(R)≤ 1.