Theorems · Theorem · commutative algebra
le_isUnit_iff_zero_notMem
∀ {R : Type u_1} [inst : CommSemiring R] [Ring.KrullDimLE 0 R] [IsLocalRing R] {M : Submonoid R},
M ≤ IsUnit.submonoid R ↔ 0 ∉ M- Defined in
- Mathlib.RingTheory.KrullDimension.Zero
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Submonoidstatement and proof · cited by 3,086
- IsUnitproof · cited by 1,602
- IsLocalRingstatement and proof · cited by 339
- IsNilpotentproof · cited by 248
- List.TFAE.outproof · cited by 177
- Ring.KrullDimLEstatement and proof · cited by 79
- IsUnit.submonoidstatement and proof · cited by 56
- Iff.not_leftproof · cited by 49
- pow_memproof · cited by 46
- not_isUnit_zeroproof · cited by 20
- Ring.krullDimLE_zero_and_isLocalRing_tfaeproof · cited by 7
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