Theorems · Theorem · commutative algebra
IsLocalRing.isRegular_of_perm
∀ {R : Type u_1} {M : Type u_3} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsLocalRing R]
[IsNoetherian R M] {rs rs' : List R},
RingTheory.Sequence.IsRegular M rs → rs.Perm rs' → RingTheory.Sequence.IsRegular M rs'- Cited by
- 0 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Top.topproof · cited by 9,680
- Idealproof · cited by 4,748
- Set.extproof · cited by 2,266
- Ideal.spanproof · cited by 948
- IsLocalRingstatement and proof · cited by 339
- IsNoetherianstatement and proof · cited by 208
- Ideal.subset_spanproof · cited by 86
- RingTheory.Sequence.IsWeaklyRegularproof · cited by 40
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