Theorems · Definition · commutative algebra
Subsemiring.subtype
{R : Type u} → [inst : NonAssocSemiring R] → (s : Subsemiring R) → ↥s →+* RThe natural ring hom from a subsemiring of semiring R to R.
- Defined in
- Mathlib.Algebra.Ring.Subsemiring.Defs
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
- Assumes
- NonAssocSemiring
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.
- RingHomstatement · cited by 10,189
- MonoidHomproof · cited by 3,629
- AddMonoidHomproof · cited by 3,230
- NonAssocSemiringstatement and proof · cited by 805
- Subsemiringstatement and proof · cited by 456
- Subsemiring.toSubmonoidproof · cited by 153
- AddSubmonoid.subtypeproof · cited by 28
- Submonoid.subtypeproof · cited by 26
- Subsemiring.toAddSubmonoidproof · cited by 20
Cited by14
Results whose statement or proof uses this declaration.
- Subsemiring.inclusionproof · cited by 5
- IsArtinianRing.isUnit_of_isIntegral_of_nonZeroDivisorproof · cited by 2
- Subalgebra.mem_of_finsetSum_eq_one_of_pow_smul_memproof · cited by 2
- RingEquiv.ofLeftInverseSproof · cited by 2
- Subsemiring.subtype_injectivestatement · cited by 2
- Subsemiring.rangeS_subtypestatement and proof · cited by 1
- Ideal.Quotient.stabilizerHomSurjectiveAuxFunctorproof · cited by 1
- Subalgebra.toSubsemiring_subtypestatement · cited by 1
- Subalgebra.coe_valAstatement · cited by 0
- Subalgebra.coe_valA'statement · cited by 0
- Algebra.algebraMap_ofSubsemiringstatement · cited by 0
- Subsemiring.coe_subtypestatement · cited by 0