Theorems · Theorem · commutative algebra
RingHom.IsIntegralElem.add
∀ {R : Type u_1} {S : Type u_4} [inst : CommRing R] [inst_1 : CommRing S] (f : R →+* S) {x y : S},
f.IsIntegralElem x → f.IsIntegralElem y → f.IsIntegralElem (x + y)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- RingHomstatement and proof · cited by 10,189
- Subring.closureproof · cited by 78
- RingHom.IsIntegralElemstatement and proof · cited by 33
- Subring.subset_closureproof · cited by 18
- Subring.add_memproof · cited by 6
- RingHom.IsIntegralElem.of_mem_closureproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- IsIntegral.addproof · cited by 6
- RingHom.IsIntegralElem.subproof · cited by 2
- MvPolynomial.finite_universalFactorizationMapproof · cited by 0