Theorems · Theorem · commutative algebra
Subring.zero_mem
∀ {R : Type u} [inst : NonAssocRing R] (s : Subring R), 0 ∈ sA subring contains the ring's 0.
- Defined in
- Mathlib.Algebra.Ring.Subring.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext
- Assumes
- NonAssocRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Subringstatement and proof · cited by 602
- NonAssocRingstatement and proof · cited by 483
- ZeroMemClass.zero_memproof · cited by 162
Cited by7
Results whose statement or proof uses this declaration.
- ValuationSubring.zero_memproof · cited by 2
- Algebra.adjoin_eq_ring_closureproof · cited by 2
- FreeCommRing.isSupported_zeroproof · cited by 1
- JacobsonNoether.exists_separable_and_not_isCentralproof · cited by 1
- Subring.exists_le_valuationSubring_of_isIntegrallyClosedInproof · cited by 1
- Subring.comap_map_eqproof · cited by 1
- LocalSubring.exists_le_valuationSubring_of_isIntegrallyClosedInproof · cited by 1