The Krull-Gabriel Dimension of Cycle-Finite Artin Algebras Page 1 Algebr Represent Theor (2016)
19:215–233 DOI 10.1007/s10468-015-9571-6 The Krull-Gabriel Dimension of Cycle-Finite Artin …

Let Λ be an artin algebra (this means that Λ is a module-finite k-algebra, where k is an
artinian commutative ring). The modules to be considered will be left Λ-modules of finite …

Abstract For an Artin Algebra Λ of finite representation type, the category Λ-mod, considered
as a ring with several objects, has Krull dimension zero. Contrary, for a wild hereditary Artin …

FINITENESS OF REPRESENTATION DIMENSION M. Auslander introduced a concept of
representation dimension of artin algebras in [A], w Page 1 PROCEEDINGS OF THE …

As is shown in r9] for a tame hereditary Artin Algebra A, the category A-mod, considered as a
ring with several objects has Krull dimension two. This means that the category F of all …

Lower bounds for the dimension of a triangulated category are provided. These bounds are
applied to stable derived categories of Artin algebras and of commutative complete …

We characterize the finiteness of the representation type of an artin algebra in terms of the
behavior of the projective covers and the injective envelopes of the simple modules with …

EUDML | Cycle-finite algebras with almost all indecomposable modules of projective or
injective dimension at most one Skip to main content (access key 's'), Skip to navigation (access …

O. Introduction Tame hereditary Artin algebras have a lot of nice homological properties: For
instance, the categories P, Rand 1 consisting of all preprojective, regular and preinjective …

We prove that an artin algebra is of finite representation type if and only if almost all finitely
generated indecomposable-modules are cycle-finite. Moreover, we prove that every cycle …