CONTENTSIntroduction............................................................................................................................................51. Cohen schemes.................................................................................................................................72. Projective abelian Hopf algebras......................................................................................................113. The structure of groups ..............................................................................174....
Let A be an artin algebra over a commutative artin ring R and ind A the category of indecomposable finitely generated right A-modules. Denote
to be the full subcategory of ind A formed by the modules X whose all predecessors in ind A have projective dimension at most one, and by
the full subcategory of ind A formed by the modules X whose all successors in ind A have injective dimension at most one. Recently, two classes of artin algebras A with
co-finite in ind A, quasi-tilted algebras and...
We construct arbitrarily complicated indecomposable finite-dimensional modules with periodic syzygies over symmetric algebras.
We introduce a new wide class of finite-dimensional algebras which admit families of standard stable tubes (in the sense of Ringel [17]). In particular, we prove that there are many algebras of arbitrary nonzero (finite or infinite) global dimension whose Auslander-Reiten quivers admit faithful standard stable tubes.
CONTENTS1. Introduction.............52. Basic dimension of artin rings................73. Cobasic dimension of artin rings............84. Basic dimension of algebras stably equivalent to an hereditary artin algebra............125. Hereditary artin algebras of global basic and cobasic dimension 1....................176. Global basic and cobasic dimensions of radical squared zero algebras............34References...............43
In the paper, we introduce a wide class of domestic finite dimensional algebras over an algebraically closed field which are obtained from the hereditary algebras of Euclidean type , n≥1, by iterated one-point extensions by two-ray modules. We prove that these algebras are domestic and their Auslander-Reiten quivers admit infinitely many nonperiodic connected components with infinitely many orbits with respect to the action of the Auslander-Reiten translation. Moreover, we exhibit a wide class of...
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