Vol. 100, No. 2, 1982

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Supplemented modules over Dedekind domains

Jutta Hausen

Vol. 100 (1982), No. 2, 387–402

The R-module M is said to be supplemented if every submodule of M has a minimal supplement. For R a Dedekind domain, we relate this lattice theoretical condition to direct decompositions of M, the smallness of the radical J(M) of M, the semi-simplicity and lifting of decompositions of M∕J(M), and the existence of quasi-projective covers. If M is contained in some R-module as a small submodule, M is said to be a small module. The structure of all supplemented and all small R-modules is determined and it is shown that, for R local, the smallness of J(M), the smallness of M, and M being a supplemented reduced module are equivalent conditions.

Mathematical Subject Classification 2000
Primary: 13F05
Secondary: 13C13, 16A53
Received: 6 September 1980
Revised: 28 January 1981
Published: 1 June 1982
Jutta Hausen