Theorems · Theorem · commutative algebra
IsIntegral.of_finite
∀ (R : Type u_1) {B : Type u_3} [inst : CommRing R] [inst_1 : Ring B] [inst_2 : Algebra R B] [Module.Finite R B]
(x : B), IsIntegral R x- Cited by
- 16 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Module.Finitestatement and proof · cited by 1,032
- IsIntegralstatement · cited by 427
- Algebra.IsIntegral.isIntegralproof · cited by 86
- Algebra.lmulproof · cited by 41
- isIntegral_algHom_iffproof · cited by 15
- Algebra.lmul_injectiveproof · cited by 5
Cited by16
Results whose statement or proof uses this declaration.
- IsIntegral.of_mem_of_fgproof · cited by 13
- IsAlgebraic.of_finiteproof · cited by 8
- Module.End.IsSemisimple.of_mem_adjoin_pairproof · cited by 3
- minpoly.ne_zero_of_finiteproof · cited by 3
- Field.primitive_element_iff_minpoly_natDegree_eqproof · cited by 2
- isIntegral_of_noetherianproof · cited by 2
- Field.finite_intermediateField_of_exists_primitive_elementproof · cited by 1
- irreducible_X_pow_sub_C_of_root_adjoin_eq_topproof · cited by 1
- IntermediateField.adjoin_minpoly_coeff_of_exists_primitive_elementproof · cited by 1
- Module.End.IsSemisimple.aevalproof · cited by 1
- Polynomial.Gal.prime_degree_dvd_cardproof · cited by 1
- trace_eq_finrank_mul_minpoly_nextCoeffproof · cited by 1