Projective cover
= Projective cover
{title2=$P(M)$}
{wiki}
A projective cover of a module $M$ is an essential surjection $P\twoheadrightarrow M$ from a <projective module>. For a finite-dimensional algebra, every finite-dimensional module has one; the projective cover of a simple module is indecomposable and has that simple module as its head.