International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 3, Pages 545-548
doi:10.1155/S0161171285000588
Semi-perfect and F-semi-perfect modules
Department of Mathematics and Statistics, University of Guelph, Guelph N1G 2W1, Ontario, Canada
Received 5 February 1985
Copyright © 1985 David J. Fieldhouse. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.