Theorems · Theorem · commutative algebra
rank_polynomial_polynomial
∀ (R : Type u_1) (S : Type u_2) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] [NoZeroDivisors R], Module.rank (Polynomial R) (Polynomial S) = Module.rank R S
- Defined in
- Mathlib.RingTheory.Algebraic.Integral
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Polynomialstatement and proof · cited by 5,681
- Cardinalstatement · cited by 2,598
- NoZeroDivisorsstatement and proof · cited by 545
- Module.rankstatement · cited by 496
- Polynomial.algebrastatement · cited by 19
- Algebra.isPushout_iffproof · cited by 5
- IsBaseChange.rank_eqproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- RatFunc.rank_ratFunc_ratFuncproof · cited by 1
- Algebra.IsAlgebraic.rank_fractionRing_polynomialproof · cited by 0