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Theorems · Theorem · commutative algebra

Ideal.ne_top_iff_of_liesOver

∀ {A : Type u_2} [inst : CommSemiring A] {B : Type u_3} [inst_1 : Semiring B] [inst_2 : Algebra A B] (P : Ideal B)
  (p : Ideal A) [P.LiesOver p], P ≠ ⊤ ↔ p ≠ ⊤
Defined in
Mathlib.RingTheory.Ideal.Over
Cited by
1 results in Mathlib
Foundations
Depth 31 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringSemiringAlgebraIdeal.LiesOver
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Around this declaration

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Ideal.Quotient.nontrivial_of_liesOver_of_ne_top · cited by 1Quotient.nontrivial_of_li…Semiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringTop.top · cited by 9680Top.topIdeal · cited by 4748IdealIdeal.LiesOver · cited by 272Ideal.LiesOverIff.ne · cited by 52Iff.neIdeal.eq_top_iff_of_liesOver · cited by 2Ideal.eq_top_iff_of_liesO…Ideal.ne_top_iff_of_liesOverCITED BYCITES

Cites8

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Cited by1

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