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Semi-perfect and F -semi-perfect modules

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  • David J. Fieldhouse

Abstract

A module is semi-perfect iff every factor module has a projective cover. A module M = A + B (for submodules A and B ) is amply supplemented iff there exists a submodule A ′ (called a supplement of A ) of B such M = A + A ′ and A ′ is minimal with this property. If B = M then M is supplemented. Kasch and Mares [1] have shown that the first and last of these conditions are equivalent for projective modules. Here it is shown that an arbitrary module is semi-perfect iff it is (amply) supplemented by supplements which have projective covers, an extension of the result of Kasch and Mares [1]. Corresponding results are obtained for F -semi-perfect modules.

Suggested Citation

  • David J. Fieldhouse, 1985. "Semi-perfect and F -semi-perfect modules," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 8, pages 1-4, January.
    • Handle: RePEc:hin:jijmms:313204
    DOI: 10.1155/S0161171285000588
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