… of hereditary algebras in terms of the growth number [16]. The main purpose of this paper is
to describe all artin algebras for which every indecomposable projective module is directing. …

… for an artin algebra the category of finitely generated Gorensteinprojective modules. Such …
of Gorenstein-projective modules over a CM-finite Gorenstein artin algebra is the simplest one …

… Artin algebra with this property as an Artin algebra satisfying the irreducible mapping property
for preprojective modules … general for Artin algebras, a 11 preprojective modules need not …

… R of projective modules. We consider R-bimodules of the form M= V/P, where V = R” is the
module … Then P is projective and of rank d as left module if I,-, = R and In-,,+, = 0. The converse …

… In this paper the PHI algebras (more precisely right PHI algebras) are algebras which are …
indecomposable projective module is hereditary projective or injective. The PHI algebras were …

… 23() ARTIN A NIX ZHANG We define the associated projective scheme to be the pair proj A
… and / is the object determined by the right module A , . We also have the autoequivalence s of …

… Applying induction to the 0/aO3-projective module P/FP, we see that the latter is generated
by (n - 1 - r) . r + 1/2 [r(r + 3)] elements, if r ? n - 1, and by 1 + 1/2[(n - 1)(n + 2)] elements if r = n…

… algebras we prove that, for a loop-finite artin algebra A, the … ; (iii) There is a generic A -module;
and (iv) The Auslander—… has only finitely many projective modules, we conclude that …