Theorems · Theorem · commutative algebra

LinearEquiv.map_ne_zero_iff

∀ {R : Type u_1} {S : Type u_6} {M : Type u_7} {M₂ : Type u_9} [inst : Semiring R] [inst_1 : Semiring S]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] {module_M : Module R M} {module_S_M₂ : Module S M₂}
  {σ : R →+* S} {σ' : S →+* R} {re₁ : RingHomInvPair σ σ'} {re₂ : RingHomInvPair σ' σ} (e : M ≃ₛₗ[σ] M₂) {x : M},
  e x ≠ 0 ↔ x ≠ 0

Defined in

Mathlib.Algebra.Module.Equiv.Defs

Cited by

6 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoid