Theorems · Theorem · commutative algebra
Submodule.map_unop_one
∀ {R : Type u} [inst : CommSemiring R] {A : Type v} [inst_1 : Semiring A] [inst_2 : Algebra R A],
Submodule.map (↑(MulOpposite.opLinearEquiv R).symm) 1 = 1- Defined in
- Mathlib.Algebra.Algebra.Operations
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
Around this declaration
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Cites12
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 · cited by 1,461
- LinearEquiv.toLinearMapstatement · cited by 1,171
- MulOppositestatement · cited by 1,135
- Submodule.mapstatement · cited by 614
- MulOpposite.opLinearEquivstatement and proof · cited by 44
- Submodule.comap_equiv_eq_map_symmproof · cited by 12
- Submodule.comap_op_oneproof · cited by 1
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