A left module is a generalization of a vector space over a field, where the scalars are the elements of a ring (not necessarily commutative).
A left module has left multiplication by scalars. Let V be an abelian group (with additive notation) and R the scalar ring, we have the following laws for x, y in V and r, s in R:
1. r *: (x + y) = r *: x + r *: y
2. (r + s) *: x = r *: x + s *: x
3. (r * s) *: x = r *: (s *: x)
4. R.one * x = x
- Type Params
- R
Scalar type
- V
Abelian group type
- Companion
- object
trait AdditiveCommutativeGroup[V]
trait AdditiveCommutativeMonoid[V]
trait AdditiveCommutativeSemigroup[V]
trait AdditiveGroup[V]
trait AdditiveMonoid[V]
trait AdditiveSemigroup[V]
trait Serializable
class Any
trait PolynomialOverField[C]
trait ZAlgebra[V]
trait PolynomialOverCRing[C]
class ArrayCoordinateSpace[A]
Value members
Abstract methods
Inherited methods
override
- Definition Classes
- AdditiveCommutativeGroup -> AdditiveCommutativeMonoid -> AdditiveCommutativeSemigroup -> AdditiveGroup -> AdditiveMonoid -> AdditiveSemigroup
- Inherited from
- AdditiveCommutativeGroup
Given a sequence of as, compute the sum.
Given a sequence of as, compute the sum.
- Inherited from
- AdditiveMonoid
override
- Definition Classes
- AdditiveGroup -> AdditiveMonoid -> AdditiveSemigroup
- Inherited from
- AdditiveGroup