| import OAI.Algebra.Finitistic.Ordinary.OrdinaryBlockBimodule | |
| import OAI.Algebra.Finitistic.Ordinary.OrdinaryAssociativeTensorModules | |
| namespace OAI | |
| noncomputable section | |
| namespace LittleFinitistic.BlockModule | |
| universe u | |
| /-- A module supported on the first factor of the actual product algebra. -/ | |
| def First (_k _L _R Z : Type u) := Z | |
| /-- A module supported on the second factor of the actual product algebra. -/ | |
| def Second (_k _L _R Z : Type u) := Z | |
| variable (k L R Z : Type u) [Field k] [Ring L] [Ring R] [Algebra k L] [Algebra k R] | |
| [AddCommGroup Z] [Module k Z] | |
| namespace First | |
| instance : AddCommGroup (First k L R Z) := inferInstanceAs (AddCommGroup Z) | |
| instance : Module k (First k L R Z) := inferInstanceAs (Module k Z) | |
| instance [Module L Z] : Module (L × R) (First k L R Z) := Module.compHom Z (RingHom.fst L R) | |
| instance [Module L Z] [IsScalarTower k L Z] : IsScalarTower k (L × R) (First k L R Z) where | |
| smul_assoc c d z := smul_assoc c d.1 (show Z from z) | |
| end First | |
| namespace Second | |
| instance : AddCommGroup (Second k L R Z) := inferInstanceAs (AddCommGroup Z) | |
| instance : Module k (Second k L R Z) := inferInstanceAs (Module k Z) | |
| instance [Module R Z] : Module (L × R) (Second k L R Z) := Module.compHom Z (RingHom.snd L R) | |
| instance [Module R Z] [IsScalarTower k R Z] : IsScalarTower k (L × R) (Second k L R Z) where | |
| smul_assoc c d z := smul_assoc c d.2 (show Z from z) | |
| end Second | |
| end LittleFinitistic.BlockModule | |
| end | |
| end OAI | |