Monobrick, a uniform approach to torsion-free classes and wide subcategories

A Brick Version of a Theorem of Auslander

“…Remark 3.21. Minimal extending modules (i.e., finite-dimensional torsion-free, almost torsion modules) do not provide enough information to determine a torsion-free class in Λ-mod as already observed in [6], [16].…”

“…Since the torsion-free classes are definable, by Theorem 2.14, it is enough to prove that F ∩ Λ-mod = F ∩ Λ-mod. By [16,Th. 3.15], we know that torsion-free classes in Λ-mod are determined by their simple objects.…”

“…By [16,Th. 3.15], we know that torsion-free classes in Λ-mod are determined by their simple objects.…”

“…Remark 3.2. Modules satisfying conditions (1) and (2) in the definition above are precisely the simple torsion-free objects used in Enomoto's study of torsion-free classes [16].…”

“…Recall that a finite-dimensional module S = 0 is simple with respect to a torsion-free class (see [16]), if it satisfies conditions (1) and (2) in Definition 3.1.…”