Theorems · Theorem · commutative algebra
Submodule.map_op_mul
∀ {R : Type u} [inst : CommSemiring R] {A : Type v} [inst_1 : Semiring A] [inst_2 : Algebra R A] (M N : Submodule R A),
Submodule.map (↑(MulOpposite.opLinearEquiv R)) (M * N) =
Submodule.map (↑(MulOpposite.opLinearEquiv R)) N * Submodule.map (↑(MulOpposite.opLinearEquiv R)) M- Defined in
- Mathlib.Algebra.Algebra.Operations
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 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.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- le_antisymmproof · cited by 2,068
- LinearEquiv.symmproof · 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
- MulOpposite.opproof · cited by 520
Cited by2
Results whose statement or proof uses this declaration.
- Submodule.map_unop_mulproof · cited by 2
- Submodule.comap_unop_mulproof · cited by 0