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Theorems · Theorem · commutative algebra

FractionalIdeal.map_zero

∀ {R : Type u_1} [inst : CommRing R] {S : Submonoid R} {P : Type u_2} [inst_1 : CommRing P] [inst_2 : Algebra R P]
  {P' : Type u_3} [inst_3 : CommRing P'] [inst_4 : Algebra R P'] (g : P →ₐ[R] P'), FractionalIdeal.map g 0 = 0
Defined in
Mathlib.RingTheory.FractionalIdeal.Operations
Cited by
2 results in Mathlib
Foundations
Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraCommRingAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

FractionalIdeal.map_div · cited by 2FractionalIdeal.map_divFractionalIdeal.map_eq_zero_iff · cited by 0FractionalIdeal.map_eq_ze…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraAlgHom · cited by 3236AlgHomSubmonoid · cited by 3086SubmonoidFractionalIdeal · cited by 423FractionalIdealFractionalIdeal.map · cited by 20FractionalIdeal.mapFractionalIdeal.map_coeIdeal · cited by 2FractionalIdeal.map_coeId…FractionalIdeal.map_zeroCITED BYCITES

Cites7

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Cited by2

Results whose statement or proof uses this declaration.