Theorems · Theorem · commutative algebra
RingHom.isIntegralElem_map
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : Ring S] (f : R →+* S) {x : R}, f.IsIntegralElem (f x)- Cited by
- 8 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- sub_selfproof · cited by 996
- Polynomial.eval₂_Cproof · cited by 50
- Polynomial.monic_X_sub_Cproof · cited by 41
- Polynomial.eval₂_Xproof · cited by 34
- RingHom.IsIntegralElemstatement · cited by 33
- Polynomial.eval₂_subproof · cited by 23
Cited by8
Results whose statement or proof uses this declaration.
- isIntegral_algebraMapproof · cited by 15
- RingHom.isIntegral_of_surjectiveproof · cited by 7
- RingHom.isIntegral_respectsIsoproof · cited by 4
- RingHom.isIntegralElem_zeroproof · cited by 3
- RingHom.isIntegralElem_oneproof · cited by 1
- exists_isIntegral_sub_of_isIntegralElem_of_mul_mem_rangeproof · cited by 1
- PrimeSpectrum.isHomeomorph_comapproof · cited by 1
- MvPolynomial.finite_universalFactorizationMapproof · cited by 0