Theorems · Theorem · commutative algebra
Submodule.comap_op_mul
∀ {R : Type u} [inst : CommSemiring R] {A : Type v} [inst_1 : Semiring A] [inst_2 : Algebra R A]
(M N : Submodule R Aᵐᵒᵖ),
Submodule.comap (↑(MulOpposite.opLinearEquiv R)) (M * N) =
Submodule.comap (↑(MulOpposite.opLinearEquiv R)) N * Submodule.comap (↑(MulOpposite.opLinearEquiv R)) M- Defined in
- Mathlib.Algebra.Algebra.Operations
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 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.symmproof · cited by 1,461
- LinearEquiv.toLinearMapstatement and proof · cited by 1,171
- MulOppositestatement and proof · cited by 1,135
- Submodule.mapproof · cited by 614
- Submodule.comapstatement · cited by 347
- MulOpposite.opLinearEquivstatement and proof · cited by 44
- Submodule.comap_equiv_eq_map_symmproof · cited by 12
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