Theorems · Theorem · commutative algebra
Ideal.IsTwoSided.pow_add
∀ {R : Type u} [inst : Semiring R] {I : Ideal R} [I.IsTwoSided] (m n : ℕ), I ^ (m + n) = I ^ m * I ^ n- Defined in
- Mathlib.RingTheory.Ideal.Operations
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringIdeal.IsTwoSided
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Submoduleproof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- add_zeroproof · cited by 2,707
- eq_or_neproof · cited by 1,117
- Ideal.IsTwoSidedstatement and proof · cited by 179
- Submodule.pow_zeroproof · cited by 9
- Submodule.pow_addproof · cited by 3
- Ideal.IsTwoSided.mul_oneproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.IsTwoSided.pow_succproof · cited by 1