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Theorems · Theorem · commutative algebra

Subring.closure_eq

∀ {R : Type u} [inst : NonAssocRing R] (s : Subring R), Subring.closure ↑s = s

Closure of a subring S equals S.

Defined in
Mathlib.Algebra.Ring.Subring.Basic
Cited by
3 results in Mathlib
Foundations
Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NonAssocRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsFractionRing.ringHom_fieldRange_eq_of_comp_eq_of_range_eq · cited by 2IsFractionRing.ringHom_fi…Subring.comap_map_eq · cited by 1Subring.comap_map_eqSubring.closure_univ · cited by 0Subring.closure_univSetLike.coe · cited by 8199SetLike.coeSubring · cited by 602SubringNonAssocRing · cited by 483NonAssocRingSubring.closure · cited by 78Subring.closureGaloisInsertion.l_u_eq · cited by 37GaloisInsertion.l_u_eqSubring.gi · cited by 6Subring.giSubring.closure_eqCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.