2025/12/23 by Víctor Becerril, Becerril, Víctor, Marco A. Pérez +1
Mathematics · #16E10 #18G10 #18G20 #18G25 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Category Theory (math.CT) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2512.20764
openalex publication_date 2025/12/23 · openalex created_date 2025/12/26 · openalex updated_date 2026/07/28
We define and study induced duality pairs under Foxby equivalences. Given a semidualizing (S,R)-bimodule S CR, if (AC(R),BC(R\rm op)) and (AC(S\rm op),BC(S)) denote the duality pairs formed by the corresponding classes of Auslander and Bass modules, and if (M,N) is a duality pair over R, we study the duality pair formed by the essential images of the restricted Foxby equivalences (C ⊗R ∼)|AC(R) ∩ M and HomR\rm op(C,∼) |BC(R\rm op) ∩ N, denoted by MC(S) and NC(S\rm op). We investigate which additional properties of the duality pair (M,N) are transferred to (MC(S),NC(S\rm op)). We also study several versions of Gorenstein injective and Gorenstein flat modules relative to the pairs (AC(R) ∩ M,BC(R\rm op) ∩ N) and (MC(S),NC(S\rm op)). For instance, we explore the relation between these classes of modules under Foxby equivalences and under Pontryagin duality.