Theorems · Theorem · commutative algebra
Commute.isNilpotent_mul_right
∀ {R : Type u_1} {x y : R} [inst : Semiring R], Commute x y → IsNilpotent x → IsNilpotent (x * y)- Defined in
- Mathlib.RingTheory.Nilpotent.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- MulZeroClass.zero_mulproof · cited by 1,625
- Commutestatement and proof · cited by 639
- IsNilpotentstatement and proof · cited by 248
- Commute.mul_powproof · cited by 22
Cited by5
Results whose statement or proof uses this declaration.
- Commute.isNilpotent_mul_leftproof · cited by 7
- Polynomial.isNilpotent_C_mul_pow_X_of_isNilpotentproof · cited by 2
- LieAlgebra.IsKilling.eq_zero_of_isNilpotent_ad_of_mem_isCartanSubalgebraproof · cited by 1
- PowerSeries.HasSubst.mul_leftproof · cited by 0
- Commute.isNilpotent_mul_right_iffproof · cited by 0