Almost Cyclic Coherent Components of an Auslander–Reiten Quiver

Krull Dimension of Tame Generalized Multicoil Algebras

“…If s = 1, such a translation quiver is said to be a generalized coil. The admissible operations of types (ad 1), (ad 2), (ad 3), (ad 1 * ), (ad 2 * ) and (ad 3 * ) have been introduced in [2][3][4], the admissible operations (ad 4) and (ad 4 * ) for r = 0 in [16], and the admissible operations (ad 4), (ad 4 * ) for r ≥ 1, (ad 5) and (ad 5 * ) in [20,21].…”

“…For the operation (fad 1) s ≥ 0, for (fad 2) and (fad 4) s ≥ 1, and for (fad 3) s ≥ t − 1. In all above operations X s is injective (see [20] or [21] for the details).…”

“…These ten operations are called the admissible operations. Following [20] a connected translation quiver is said to be a generalized multicoil if can be obtained from a finite family T 1 , T 2 , . .…”

“…For an indecomposable brick X in , called the pivot, one defines five admissible operations (ad 1)-(ad 5) and their duals (ad 1 * )-(ad 5 * ) modifying the translation quiver = ( , τ ) to a new translation quiver ( , τ ) and the algebra A to a new algebra A , depending on the shape of the support S(X) (see [20,Section 2] for the figures illustrating the modified translation quivers ).…”

Degenerations in the module varieties of almost cyclic coherent Auslander–Reiten components

“…For an indecomposable module X in Γ , called the pivot, one defines five admissible operations (ad 1)-(ad 5) and their duals (ad 1 * )-(ad 5 * ) modifying the translation quiver Γ = (Γ, τ ) to a new translation quiver (Γ , τ ) and the algebra A to a new algebra A , depending on the shape of the support S(X) (see [21,Section 2] for figures illustrating Γ ).…”