Theorems · Definition · commutative algebra
NonUnitalSubring.toSubring
{R : Type u} → [inst : NonAssocRing R] → (S : NonUnitalSubring R) → 1 ∈ S → Subring RTurn a non-unital subring containing 1 into a subring.
- Defined in
- Mathlib.Algebra.Ring.Subring.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- 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.
- Subringstatement · cited by 602
- NonAssocRingstatement and proof · cited by 483
- AddSubmonoid.toAddSubsemigroupproof · cited by 198
- AddSubsemigroup.carrierproof · cited by 198
- NonUnitalSubringstatement and proof · cited by 185
- NonUnitalSubsemiring.toAddSubmonoidproof · cited by 56
- NonUnitalSubring.toNonUnitalSubsemiringproof · cited by 15
Cited by2
Results whose statement or proof uses this declaration.
- NonUnitalSubring.toSubring_toNonUnitalSubringstatement and proof · cited by 0
- Subring.toNonUnitalSubring_toSubringstatement and proof · cited by 0