Theorems · Theorem · commutative algebra
IsNilpotent.isUnit_add_left_of_commute
∀ {R : Type u_1} [inst : Ring R] {r u : R}, IsNilpotent r → IsUnit u → Commute r u → IsUnit (u + r)- Defined in
- Mathlib.RingTheory.Nilpotent.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- Commutestatement and proof · cited by 639
- add_mulproof · cited by 363
- IsUnit.unitproof · cited by 252
- IsNilpotentstatement and proof · cited by 248
- Units.isUnitproof · cited by 116
- IsUnit.mul_val_invproof · cited by 29
- Units.isUnit_mul_unitsproof · cited by 3
- Commute.units_inv_rightproof · cited by 3
- IsUnit.isNilpotent_mul_unit_of_commute_iffproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.isUnit_aeval_of_isUnit_aeval_of_isNilpotent_subproof · cited by 2
- IsNilpotent.isUnit_add_right_of_commuteproof · cited by 2
- Polynomial.isUnit_of_coeff_isUnit_isNilpotentproof · cited by 2
- Polynomial.existsUnique_nilpotent_sub_and_aeval_eq_zeroproof · cited by 1