algebra

ring

package ring

Visibility
  1. Public
  2. All

Type Members

  1. trait AdditiveCommutativeGroup[A] extends AdditiveGroup[A] with AdditiveCommutativeMonoid[A]

  2. trait AdditiveCommutativeMonoid[A] extends AdditiveMonoid[A] with AdditiveCommutativeSemigroup[A]

  3. trait AdditiveCommutativeSemigroup[A] extends AdditiveSemigroup[A]

  4. trait AdditiveGroup[A] extends AdditiveMonoid[A]

  5. trait AdditiveGroupFunctions[G[T] <: AdditiveGroup[T]] extends AdditiveMonoidFunctions[G]

  6. trait AdditiveMonoid[A] extends AdditiveSemigroup[A]

  7. trait AdditiveMonoidFunctions[M[T] <: AdditiveMonoid[T]] extends AdditiveSemigroupFunctions[M]

  8. trait AdditiveSemigroup[A] extends Serializable

  9. trait AdditiveSemigroupFunctions[S[T] <: AdditiveSemigroup[T]] extends AnyRef

  10. trait BoolRing[A] extends BoolRng[A] with CommutativeRing[A]

    A Boolean ring is a ring whose multiplication is idempotent, that is a⋅a = a for all elements a.

  11. trait BoolRng[A] extends CommutativeRng[A]

    A Boolean rng is a rng whose multiplication is idempotent, that is a⋅a = a for all elements a.

  12. trait CommutativeRig[A] extends Rig[A] with CommutativeSemiring[A] with MultiplicativeCommutativeMonoid[A]

    CommutativeRig is a Rig that is commutative under multiplication.

  13. trait CommutativeRing[A] extends Ring[A] with CommutativeRig[A] with CommutativeRng[A]

    CommutativeRing is a Ring that is commutative under multiplication.

  14. trait CommutativeRng[A] extends Rng[A] with CommutativeSemiring[A]

    CommutativeRng is a Rng that is commutative under multiplication.

  15. trait CommutativeSemiring[A] extends Semiring[A] with MultiplicativeCommutativeSemigroup[A]

    CommutativeSemiring is a Semiring that is commutative under multiplication.

  16. trait Field[A] extends CommutativeRing[A] with MultiplicativeCommutativeGroup[A]

  17. trait FieldFunctions[F[T] <: Field[T]] extends RingFunctions[F] with MultiplicativeGroupFunctions[F]

  18. trait MultiplicativeCommutativeGroup[A] extends MultiplicativeGroup[A] with MultiplicativeCommutativeMonoid[A]

  19. trait MultiplicativeCommutativeMonoid[A] extends MultiplicativeMonoid[A] with MultiplicativeCommutativeSemigroup[A]

  20. trait MultiplicativeCommutativeSemigroup[A] extends MultiplicativeSemigroup[A]

  21. trait MultiplicativeGroup[A] extends MultiplicativeMonoid[A]

  22. trait MultiplicativeGroupFunctions[G[T] <: MultiplicativeGroup[T]] extends MultiplicativeMonoidFunctions[G]

  23. trait MultiplicativeMonoid[A] extends MultiplicativeSemigroup[A]

  24. trait MultiplicativeMonoidFunctions[M[T] <: MultiplicativeMonoid[T]] extends MultiplicativeSemigroupFunctions[M]

  25. trait MultiplicativeSemigroup[A] extends Serializable

  26. trait MultiplicativeSemigroupFunctions[S[T] <: MultiplicativeSemigroup[T]] extends AnyRef

  27. trait Rig[A] extends Semiring[A] with MultiplicativeMonoid[A]

    Rig consists of:

  28. trait Ring[A] extends Rig[A] with Rng[A]

    Ring consists of:

  29. trait RingFunctions[R[T] <: Ring[T]] extends AdditiveGroupFunctions[R] with MultiplicativeMonoidFunctions[R]

  30. trait Rng[A] extends Semiring[A] with AdditiveCommutativeGroup[A]

    Rng (pronounced "Rung") consists of:

  31. trait Semiring[A] extends AdditiveCommutativeMonoid[A] with MultiplicativeSemigroup[A]

    Semiring consists of:

Value Members

  1. object AdditiveCommutativeGroup extends AdditiveGroupFunctions[AdditiveCommutativeGroup] with Serializable

  2. object AdditiveCommutativeMonoid extends AdditiveMonoidFunctions[AdditiveCommutativeMonoid] with Serializable

  3. object AdditiveCommutativeSemigroup extends AdditiveSemigroupFunctions[AdditiveCommutativeSemigroup] with Serializable

  4. object AdditiveGroup extends AdditiveGroupFunctions[AdditiveGroup] with Serializable

  5. object AdditiveMonoid extends AdditiveMonoidFunctions[AdditiveMonoid] with Serializable

  6. object AdditiveSemigroup extends AdditiveSemigroupFunctions[AdditiveSemigroup] with Serializable

  7. object BoolRing extends RingFunctions[BoolRing] with Serializable

  8. object BoolRng extends AdditiveGroupFunctions[BoolRng] with MultiplicativeSemigroupFunctions[BoolRng] with Serializable

  9. object CommutativeRig extends AdditiveMonoidFunctions[CommutativeRig] with MultiplicativeMonoidFunctions[CommutativeRig] with Serializable

  10. object CommutativeRing extends RingFunctions[CommutativeRing] with Serializable

  11. object CommutativeRng extends AdditiveGroupFunctions[CommutativeRng] with MultiplicativeSemigroupFunctions[CommutativeRng] with Serializable

  12. object CommutativeSemiring extends AdditiveMonoidFunctions[CommutativeSemiring] with MultiplicativeSemigroupFunctions[CommutativeSemiring] with Serializable

  13. object Field extends FieldFunctions[Field] with Serializable

  14. object MultiplicativeCommutativeGroup extends MultiplicativeGroupFunctions[MultiplicativeCommutativeGroup] with Serializable

  15. object MultiplicativeCommutativeMonoid extends MultiplicativeMonoidFunctions[MultiplicativeCommutativeMonoid] with Serializable

  16. object MultiplicativeCommutativeSemigroup extends MultiplicativeSemigroupFunctions[MultiplicativeCommutativeSemigroup] with Serializable

  17. object MultiplicativeGroup extends MultiplicativeGroupFunctions[MultiplicativeGroup] with Serializable

  18. object MultiplicativeMonoid extends MultiplicativeMonoidFunctions[MultiplicativeMonoid] with Serializable

  19. object MultiplicativeSemigroup extends MultiplicativeSemigroupFunctions[MultiplicativeSemigroup] with Serializable

  20. object Rig extends AdditiveMonoidFunctions[Rig] with MultiplicativeMonoidFunctions[Rig] with Serializable

  21. object Ring extends RingFunctions[Ring] with Serializable

  22. object Rng extends AdditiveGroupFunctions[Rng] with MultiplicativeSemigroupFunctions[Rng] with Serializable

  23. object Semiring extends AdditiveMonoidFunctions[Semiring] with MultiplicativeSemigroupFunctions[Semiring] with Serializable

Ungrouped