On modules with lifting properties

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Description

We have studied the lifiting property on a direct sum of completely indecomposable and cyclic hollow modules over a ring R in [8]. In this note, we shall define the lifting property of decompositions with finite direct summands in § 1 and give characterizations of this in terms of endomorphism rings of R-modules in §2. We shall study, in §3, R-modules with lifting properties and show that they are very closed to R-modules with direct decomposition of completely indecomposable and cyclic hollow modules when R is right noetherian. We shall give the dual results for the extending property and its applications in the forthcoming papers.

Journal

  • Osaka Journal of Mathematics

    Osaka Journal of Mathematics 19 (1), 189-201, 1982

    Osaka University and Osaka City University, Departments of Mathematics

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