Vol. 37, No. 1, 1971

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Characterization of the endomorphism rings of divisible torsion modules and reduced complete torsion-free modules over complete discrete valuation rings

Wolfgang Liebert

Vol. 37 (1971), No. 1, 141–170

Let R be a complete discrete valuation ring (possibly non-commutative). If K is the quotient field of R then there is an isomorphism between the category of divisible torsion R-modules G and the category of reduced complete torsionfree R-modules H given by G H = HomR(K∕R,G). Moreover, the R-endomorphism ring E(G) is naturally isomorphic to the R-endomorphism ring E(H) of H. It is the purpose of this paper to find necessary and sufficient conditions for an abstract ring to be isomorphic to the R-endomorphism ring of such an R-module.

Mathematical Subject Classification 2000
Primary: 16A64
Secondary: 13C99, 16A04
Received: 22 September 1969
Published: 1 April 1971
Wolfgang Liebert