International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 1, Pages 185-192
doi:10.1155/S0161171296000269

Projective covers and minimal free resolutions

Abstract

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.