Almost Projective Modules Over Non-Hereditary Algebras

We investigate almost projective modules over non-hereditary algebras. The proper submodules of these modules have a projective type behavior. We prove that there exists a non-hereditary algebra such that the proper submodules of their almost projective modules are actually projective. We also show that an algebra of finite representation type and its opposite algebra do not always have the same number of indecomposable almost projective modules.