Cotorsion Pairs Associated with Auslander Categories

We prove that the Auslander class determined by a semidualizing module is the left half of a perfect cotorsion pair. We also prove that the Bass class determined by a semidualizing module is preenveloping. 0. Introduction The notion of semidualizing modules over commutative noetherian rings goes back to Foxby [11] and Golod [13]. Christensen [3] extended this notion to semidualizing complexes. A semidualizing module or complex C over a commutative noetherian ring gives rise to two full subcategories of the derived category of the category of R–modules, namely the so-called Auslander class and Bass class defined by Avramov–Foxby [1, (3.1)] and Christensen [3, def. (4.1)]. Semidualizing complexes and their Auslander/Bass classes have caught the attention of several authors, see for example [1,3–5,8, 10–12,14, 16, 17]. Usually, one is interested in studying themodules in the Auslander/Bass classes (by definition, the objects of these categories are complexes), and in this paper we use AC and BC to denote the categories of all modules belonging to the Auslander class and Bass class, respectively. We mention that when C itself is a (semidualizing) module then one can describe AC and BC in terms of vanishing of certain derived module functors and invertibility of certain module homomorphisms, see Avramov–Foxby [1, prop. (3.4)] and Christensen [3, obs. (4.10)]. 2000 Mathematics Subject Classification. 13D05, 13D07, 13D25.