Theorems · Theorem · commutative algebra
Ideal.map_prodComm_prod
∀ {R : Type u} {S : Type v} [inst : Semiring R] [inst_1 : Semiring S] (I : Ideal R) (J : Ideal S),
Ideal.map (↑RingEquiv.prodComm) (I.prod J) = J.prod I- Defined in
- Mathlib.RingTheory.Ideal.Prod
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- RingHomstatement · cited by 10,189
- Idealstatement and proof · cited by 4,748
- RingEquivstatement · cited by 1,147
- RingHomClass.toRingHomstatement and proof · cited by 746
- Ideal.mapstatement and proof · cited by 692
- RingHom.sndproof · cited by 39
- Ideal.map_mapproof · cited by 37
- RingHom.fstproof · cited by 36
- Ideal.prodstatement and proof · cited by 28
- RingEquiv.prodCommstatement and proof · cited by 7
- Ideal.ideal_prod_eqproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.isPrime_of_isPrime_prod_top'proof · cited by 1
- Ideal.isPrime_ideal_prod_top'proof · cited by 1