Theorems · Theorem · ring theory
TwoSidedIdeal.mem_span_iff_mem_addSubgroup_closure
∀ {R : Type u_1} [inst : Ring R] {s : Set R} {z : R},
z ∈ TwoSidedIdeal.span s ↔ z ∈ AddSubgroup.closure (Set.univ * s * Set.univ)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
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Cites18
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
- Ringstatement and proof · cited by 7,463
- Set.univstatement and proof · cited by 3,945
- mul_oneproof · cited by 3,885
- AddSubgroupstatement · cited by 3,232
- one_mulproof · cited by 2,841
- mul_assocproof · cited by 1,667
- Set.mem_univproof · cited by 416
- Set.mulstatement · cited by 297
- AddSubgroup.closurestatement · cited by 156
- TwoSidedIdealstatement · cited by 151
- TwoSidedIdeal.spanstatement and proof · cited by 9
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