Theorems · Theorem · commutative algebra
Module.Finite.equiv
∀ {R : Type u_1} {M : Type u_4} {N : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
[inst_3 : AddCommMonoid N] [inst_4 : Module R N] [Module.Finite R M] (e : M ≃ₗ[R] N), Module.Finite R N- Defined in
- Mathlib.RingTheory.Finiteness.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearEquivstatement and proof · cited by 3,317
- LinearEquiv.toLinearMapproof · cited by 1,171
- Module.Finitestatement and proof · cited by 1,032
- LinearEquiv.surjectiveproof · cited by 66
- Module.Finite.of_surjectiveproof · cited by 29
Cited by20
Results whose statement or proof uses this declaration.
- Module.Flat.rTensor_preserves_injective_linearMapproof · cited by 24
- LinearEquiv.finiteDimensionalproof · cited by 11
- OrzechProperty.injective_of_surjective_of_injectiveproof · cited by 5
- Submodule.CoFG.of_leproof · cited by 4
- Module.Finite.equiv_iffproof · cited by 3
- InfiniteGalois.restrictNormalHom_continuousproof · cited by 1
- LinearMap.trace_eq_sum_trace_restrict_of_eq_biSupproof · cited by 1
- Submodule.CoFG.fg_of_isComplproof · cited by 1
- Module.Finite.of_equiv_equivproof · cited by 1
- IsSimpleRing.exists_algEquiv_matrix_divisionRing_finiteproof · cited by 1
- FunctionField.finiteDimensional_ratFunc_of_constantExtensionproof · cited by 1
- Module.IsStablyFree.of_free_prodproof · cited by 1