Theorems · Theorem · commutative algebra
Subalgebra.rank_sup_eq_rank_right_mul_rank_of_free
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (A B : Subalgebra R S)
[Module.Free R ↥B] [Module.Free ↥B ↥(Algebra.adjoin ↥B ↑A)],
Module.rank R ↥(A ⊔ B) = Module.rank R ↥B * Module.rank ↥B ↥(Algebra.adjoin ↥B ↑A)- Defined in
- Mathlib.Algebra.Algebra.Subalgebra.Rank
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- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
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- SetLike.coestatement and proof · cited by 8,199
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- sup_commproof · cited by 165
- Subalgebra.rank_sup_eq_rank_left_mul_rank_of_freeproof · cited by 2
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