Theorems · Theorem · commutative algebra
Submodule.map_unop_pow
∀ {R : Type u} [inst : CommSemiring R] {A : Type v} [inst_1 : Semiring A] [inst_2 : Algebra R A] (n : ℕ)
(M : Submodule R Aᵐᵒᵖ),
Submodule.map (↑(MulOpposite.opLinearEquiv R).symm) (M ^ n) =
Submodule.map (↑(MulOpposite.opLinearEquiv R).symm) M ^ n- Defined in
- Mathlib.Algebra.Algebra.Operations
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement and proof · cited by 7,192
- LinearEquiv.symmstatement and proof · cited by 1,461
- LinearEquiv.toLinearMapstatement and proof · cited by 1,171
- MulOppositestatement and proof · cited by 1,135
- Submodule.mapstatement and proof · cited by 614
- Submodule.comapproof · cited by 347
- MulOpposite.opLinearEquivstatement and proof · cited by 44
- Submodule.comap_equiv_eq_map_symmproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- CliffordAlgebra.submodule_map_pow_reverseproof · cited by 2