Theorems · Definition · commutative algebra
Subring.gi
(R : Type u) → [inst : NonAssocRing R] → GaloisInsertion Subring.closure SetLike.coe
closure forms a Galois insertion with the coercion to set.
- Defined in
- Mathlib.Algebra.Ring.Subring.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
- Subring.closurestatement and proof · cited by 78
- GaloisInsertionstatement · cited by 35
- Subring.closure_leproof · cited by 14
Cited by6
Results whose statement or proof uses this declaration.
- RingHom.map_closureproof · cited by 4
- Subring.closure_eqproof · cited by 3
- Subring.closure_unionproof · cited by 2
- Subring.closure_iUnionproof · cited by 0
- Subring.closure_sUnionproof · cited by 0
- Subring.closure_emptyproof · cited by 0