The purpose of this paper is to further the study of countably thick modules via weak injectivity. Among others, for some classes of modules in we study when direct sums of modules from satisfies a property in . In particular, we get characterization of locally countably thick modules, a generalization of locally q.f.d. modules.
In our recent paper (J. Algebra 345 (2011)) we prove that the deformed preprojective algebras of generalized Dynkin type ₙ (in the sense of our earlier work in Trans. Amer Math. Soc. 359 (2007)) are exactly (up to isomorphism) the stable Auslander algebras of simple plane singularities of Dynkin type . In this article we complete the picture by showing that the deformed mesh algebras of Dynkin type ℂₙ are isomorphic to the canonical mesh algebras of type ℂₙ, and hence to the stable Auslander algebras...
Let Λ be an artin algebra. We prove that for each sequence of non-negative integers there are only a finite number of isomorphism classes of indecomposables , the bounded derived category of Λ, with for all i ∈ ℤ and E(X) the endomorphism ring of X in if and only if , the bounded derived category of the category of all left Λ-modules, has no generic objects in the sense of [4].
We complete the derived equivalence classification of all weakly symmetric algebras of domestic type over an algebraically closed field, by solving the problem of distinguishing standard and nonstandard algebras up to stable equivalence, and hence derived equivalence. As a consequence, a complete stable equivalence classification of weakly symmetric algebras of domestic type is obtained.
In this paper, we introduce related comparability for exchange ideals. Let be an exchange ideal of a ring . If satisfies related comparability, then for any regular matrix , there exist left invertible and right invertible such that for idempotents .