Theorems · Definition · commutative algebra
Subsemiring.comap
{R : Type u} →
{S : Type v} → [inst : NonAssocSemiring R] → [inst_1 : NonAssocSemiring S] → (R →+* S) → Subsemiring S → Subsemiring RThe preimage of a subsemiring along a ring homomorphism is a subsemiring.
- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- RingHomstatement and proof · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Set.preimageproof · cited by 4,946
- Submonoidproof · cited by 3,086
- AddSubmonoidproof · cited by 1,178
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement and proof · cited by 456
- MonoidHomClass.toMonoidHomproof · cited by 294
- AddMonoidHomClass.toAddMonoidHomproof · cited by 232
- Submonoid.comapproof · cited by 179
- Subsemiring.toSubmonoidproof · cited by 153
Cited by21
Results whose statement or proof uses this declaration.
- Subalgebra.comapproof · cited by 23
- Subsemiring.gc_map_comapstatement · cited by 7
- Subsemiring.map_comap_eqstatement and proof · cited by 1
- Subsemiring.map_comap_eq_selfstatement and proof · cited by 1
- Subsemiring.map_equiv_eq_comap_symmstatement and proof · cited by 1
- Subsemiring.map_le_iff_le_comapstatement · cited by 1
- Subsemiring.comap_topstatement · cited by 1
- Subsemiring.mem_comapstatement · cited by 1
- Subsemiring.top_prodstatement · cited by 1
- Subsemiring.coe_comapstatement and proof · cited by 1
- Subsemiring.prod_topstatement · cited by 0
- Subalgebra.comap_toSubsemiringstatement · cited by 0