Theorems · Theorem · commutative algebra
Subring.comap_map_eq
∀ {R : Type u} {S : Type v} [inst : NonAssocRing R] [inst_1 : NonAssocRing S] (f : R →+* S) (s : Subring R),
Subring.comap f (Subring.map f s) = s ⊔ Subring.closure (⇑f ⁻¹' {0})- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRingNonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- RingHomstatement and proof · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Set.preimagestatement and proof · cited by 4,946
- LE.le.transproof · cited by 3,151
- le_antisymmproof · cited by 2,068
- sub_selfproof · cited by 996
- Subringstatement and proof · cited by 602
- map_subproof · cited by 565
- NonAssocRingstatement and proof · cited by 483
- le_of_eqproof · cited by 366
Cited by1
Results whose statement or proof uses this declaration.
- Subring.comap_map_eq_selfproof · cited by 0