Biserial principal ideals under algebra equivalence

An algebra equivalence induces an equivalence of finitely generated right-module categories and identifies corresponding principal right ideals. Intrinsic biseriality therefore transports in both directions.

theorem MagnitudeConjecture.RightModule.rightIdealFGObj_isBiserialObject_mapAlgEquiv_iff {k A B : Type u} [Field k] [Ring A] [Algebra k A] [FiniteDimensional k A] [IsNoetherianRing Aᵐᵒᵖ] [Ring B] [Algebra k B] [FiniteDimensional k B] [IsNoetherianRing Bᵐᵒᵖ] (f : A ≃ₐ[k] B) (e : A) : IsBiserialObject (rightIdealFGObj (f e)) ↔ IsBiserialObject (rightIdealFGObj e)

Corresponding principal right ideals under an algebra equivalence are intrinsically biserial simultaneously.