Theorems · Theorem · linear algebra
Module.rank_of_bijective_algebraMap
∀ {R : Type u_2} {S : Type u_3} [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : Algebra R S]
[StrongRankCondition R], Function.Bijective ⇑(algebraMap R S) → Module.rank R S = 1- Cited by
- 0 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
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
- Semiringstatement and proof · cited by 13,802
- 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
- Cardinalstatement · cited by 2,598
- Function.Bijectivestatement and proof · cited by 863
- Module.rankstatement · cited by 496
- StrongRankConditionstatement and proof · cited by 286
- Module.rank_eq_one_iff_finrank_eq_oneproof · cited by 8
- Module.finrank_of_bijective_algebraMapproof · cited by 2
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