Structures · Algebra
RingHomClass
RingHomClass F α β states that F is a type of (semi)ring homomorphisms.
You should extend this class when you extend RingHom.
This extends from both MonoidHomClass and MonoidWithZeroHomClass in
order to put the fields in a sensible order, even though
MonoidWithZeroHomClass already extends MonoidHomClass.
- Defined in
- Mathlib.Algebra.Ring.Hom.Defs
- Shape
- 3 explicit arguments
Extends3
Extended by2
Concrete types that are instances3
- OrderRingHom
- GradedRingHom
- RingHom
How is a type an instance?
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Assumed by214
- RingHomClass.toRingHom
- Ideal.comap
- RingHom.ker
- map_natCast
- eq_intCast
- eq_natCast
- map_ofNat
- Ideal.map_le_iff_le_comap
- Ideal.mem_comap
- RingHom.coe_coe
- RingHom.mem_ker
- map_intCast
- Ideal.map_span
- Ideal.comap_map_of_surjective
- Ideal.comap.congr_simp
- RingHom.injective_iff_ker_eq_bot
- eq_ratCast
- Ideal.comap_mono
- RingHom.ker_eq_comap_bot
- Ideal.mem_map_iff_of_surjective
- Ideal.map_top
- Ideal.le_comap_map
- Ideal.gc_map_comap
- Ideal.map_pow
- Ideal.comap_top
- Ideal.map_eq_bot_iff_of_injective
- Ideal.map_comap_le
- Ideal.map_comap_of_surjective
- Ideal.map_bot
- RingHom.ker.congr_simp
- Ideal.comap_isPrime
- Ideal.map_isPrime_of_surjective
- map_ratCast
- Ideal.comap_coe
- Ideal.map_mul
- Ideal.comap_isMaximal_of_surjective
- Ideal.comap_injective_of_surjective
- Ideal.ker_le_comap
- Ideal.comap_map_of_surjective'
- DirectLimit.Ring.of
- RingHom.ker_eq_bot_iff_eq_zero
- Ideal.comap_ne_top
- NormedSpace.map_exp
- RingHomClass.toRingHom.congr_simp
- Ideal.map_eq_top_or_isMaximal_of_surjective
- Ideal.map_le_of_le_comap
- Ideal.mem_image_of_mem_map_of_surjective
- Ideal.orderEmbeddingOfSurjective
- Ideal.giMapComap
- Ideal.comap_eq_top_iff