Theorems · Theorem · commutative algebra
IsLocalization.Away.mul_of_isUnit
∀ {R : Type u_1} [inst : CommSemiring R] {S : Type u_2} [inst_1 : CommSemiring S] [inst_2 : Algebra R S] (x y : R)
[IsLocalization.Away x S], IsUnit ((algebraMap R S) y) → IsLocalization.Away (x * y) S- Cited by
- 0 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsUnitstatement and proof · cited by 1,602
- IsLocalization.Awaystatement and proof · cited by 218
- Function.bijective_idproof · cited by 36
- IsLocalization.Away.mul'proof · cited by 7
- IsLocalization.away_of_isUnit_of_bijectiveproof · cited by 6
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