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216fb31 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | 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
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