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Theorems · Definition · commutative algebra

Subring.ofClass

{S : Type u_1} → {R : Type u_2} → [inst : NonAssocRing R] → [inst_1 : SetLike S R] → [SubringClass S R] → S → Subring R

The actual Subring obtained from an element of a SubringClass.

Defined in
Mathlib.Algebra.Ring.Subring.Defs
Cited by
2 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext
Assumes
NonAssocRingSetLikeSubringClass
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Subring.integralClosure_subring_le_iff · cited by 1Subring.integralClosure_s…Subring.coe_ofClass · cited by 0Subring.coe_ofClassSetLike.coe · cited by 8199SetLike.coeSetLike · cited by 1084SetLikeSubring · cited by 602SubringNonAssocRing · cited by 483NonAssocRingSubringClass · cited by 20SubringClassSubring.ofClassCITED BYCITES

Cites5

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

Cited by2

Results whose statement or proof uses this declaration.