Theorems · Theorem · commutative algebra
nilpotencyClass_zero
∀ {R : Type u_1} [inst : MonoidWithZero R] [Nontrivial R], nilpotencyClass 0 = 1- Defined in
- Mathlib.RingTheory.Nilpotent.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MonoidWithZeroNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nontrivialstatement and proof · cited by 2,416
- zero_addproof · cited by 2,366
- pow_zeroproof · cited by 1,094
- pow_oneproof · cited by 894
- MonoidWithZerostatement and proof · cited by 456
- nilpotencyClassstatement · cited by 12
- nilpotencyClass_eq_succ_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- nilpotencyClass_eq_oneproof · cited by 0