… of the well-known Auslander-Reiten sequence is based on the … for an arbitrary A-module T
and prove some fundamental … tilting theory and the Auslander-Reiten theory could be unified. …

… Let (Xo, ..., X~) be a cycle, which we may assume to be a cycle of the Auslander-Reiten
quiver. Since there is no indecomposable projective on this cycle, also (7 X o .... , z X~) is a cycle. …

… where R is the completion of R, with special emphasis on Cohen-Macaulay modules. We …
–Macaulay modules go to direct sums of almost split sequences of Cohen-Macaulay modules …

… -modules, by Ta the Auslander-Reiten quiver of A and by DTr the Auslander-Reiten operator…
In this paper we will not distinguish between an indecomposable A-module, its isomorphism …

… In Section 1 we recall the main definitions and results needed in the work; in particular
we explain the structure of the Auslander–Reiten quiver IT, of a tilted algebra A of tame …

… Auslander-Reiten component of an endotrivial module and its position in it. Then we deduce
the classification of the endotrivial modules … The best theorem in this direction was obtained …

… Auslander-Reiten component with “few” stable maps in TrD-direction is of shape ℤA ∞ . …
Finally, recall that a module M in Γ A is directing if it does not lie on any cycle of nonzero non…

… A-module we always mean a module in mod A, the category of finitely generated A-modules. …
As a step in this direction we prove that if/i is k-Gorenstein for all k and idn n < co , then LI is …

… the opposite quiver of d, and consists entirely of directing modules (see [36] and [37]). It was
proved in [38] that H admits a regular tilting module if and only if d has at least three vertices …

… , Auslander-Reiten quivers of representation-directed artinian rings will be studied in Sections
4 to 9. Representation-directed … interested in left modules and just call them modules. We …