Vol. 82, No. 2, 1979

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Kalathoor Varadarajan

Vol. 82 (1979), No. 2, 559–564

Let M be an R-module and N M. Any H M satisfying H + N = M (i) and H′⊂ H, H+ N = M H= H (ii) will be referred to as a supplement of N in M. In general N need not have a supplement in M. A module M will be said to have property (P1) if every N M has a supplemenl in M. If for every A M, N M with A + N = M, there exists a supplement H of N in M satisfying H A, we say that M has property (P2). Modules with property (P2) play an important role in our study of dual Goldie dimension. In the present paper we determine the class of rings R with the property that every M R-mod possesses property (P2). These ture out to be left perfect rings. Also the results obtained here throw more light on the differences between corank and P. Fleury’s spanning dimension.

Mathematical Subject Classification
Primary: 16A51, 16A51
Received: 10 August 1978
Published: 1 June 1979
Kalathoor Varadarajan