… and preinjective modules introduced by Diab and Ring& Our purpose in this paper is to
develop a general theory of preprojective and preinject& modules over arbitrary artin algebras. …

… We propose a new definition for the preprojective algebra as the … Given a preprojective
module P in mod(AoP), we define the preprojective algebra for P as the Z-graded algebra …

… notion of preprojective modules to hereditary tensor algebras it … For artin algebras stably
equivalent to an hereditary artin … a unique preprojective partition o{ ind A {or an artin algebra A …

… of indecomposable finitely generated A-modules, ind A = U^g/V… can be easily constructed
for hereditary artin algebras, if P,_ ¡ … preprojective modules is true for arbitrary artin algebras [3]. …

… with basic facts about covers, envelopes, preprojective modules and so on are which will be
… We also state, for the reader's convenience, the basic properties of preprojective modules …

… of ind A is called the preprojective partition for the algebra A . The purpose of this paper
is to continue the study of the preprojective partition for hereditary artin algebras started in …

… morphism A - B; then B is preprojective . We will refer to an Artin algebra with this property
as an Artin algebra satisfying the irreducible mapping property for preprojective modules . …

… Let Λ be a preprojective algebra of simply laced Dynkin type ∆. We study maximal rigidΛ-modules,
their endomorphism algebras and a mutation operation on these modules. This leads …

… -tilted algebras and generalized double tilted algebras, have … classes of algebras exhaust
the class of all artin algebras A for … T without preprojective direct summands. Obviously, there …

… modules X in ind A is equivalent to A being a tilted algebra given by preprojective tilting module
T over a hereditary artin algebra … -modules which contains an indecomposible module M …