Theorems · Theorem · commutative algebra
IsSMulRegular.of_ne_zero
∀ {R : Type u_1} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {r : R}
[Module.IsTorsionFree R M] [IsCancelMulZero R], r ≠ 0 → IsSMulRegular M r- Defined in
- Mathlib.Algebra.Module.Torsion.Free
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- Foundations
- Depth 14 from the axioms · uses no axioms
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Module.IsTorsionFreestatement and proof · cited by 600
- IsCancelMulZerostatement and proof · cited by 177
- IsSMulRegularstatement · cited by 128
- IsRegular.of_ne_zeroproof · cited by 15
- IsRegular.isSMulRegularproof · cited by 6
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