Theorems · Theorem · commutative algebra
LocalizedModule.mk_pow
∀ {R : Type u} [inst : CommSemiring R] {A : Type u_3} [inst_1 : Semiring A] [inst_2 : Algebra R A] {S : Submonoid R}
(n : ℕ) (a : A) (s : ↥S), LocalizedModule.mk a s ^ n = LocalizedModule.mk (a ^ n) (s ^ n)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Quot.sound
- Assumes
- CommSemiringSemiringAlgebra
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Cites12
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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Submonoidstatement and proof · cited by 3,086
- pow_zeroproof · cited by 1,094
- pow_succ'proof · cited by 228
- LocalizedModulestatement and proof · cited by 154
- OreLocalizationproof · cited by 90
- LocalizedModule.mkstatement and proof · cited by 73
- OreLocalization.oreDivproof · cited by 72
- OreLocalization.one_defproof · cited by 10
- LocalizedModule.mk_mul_mkproof · cited by 5
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