International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 1, Pages 185-192
Projective covers and minimal free resolutions
Department of Mathematical Sciences, The University of Akron, Akron 44325-4002, Ohio, USA
Received 9 September 1994
Copyright © 1996 Mark A. Goddard. 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.
Using a generalization of the definition of the projective cover of a module, a special type of surjective free resolution, known as the projective cover of a complex, may be defined. The projective cover is shown to be a direct summand of every surjective free resolution and to be the direct sum of the minimal free resolution and an exact complex. Necessary and sufficient conditions for the projective cover and minimal free resolution to be identical are discussed.