Numeric.Ring.Rng

Documentation

data RngRing r

The free Ring given a Rng obtained by adjoining Z, such that

 RngRing r = n*1 + r

This ring is commonly denoted r^.

Constructors

RngRing !Integer r

Instances

(Abelian r, Group r) => RightModule Integer (RngRing r)

(Abelian r, Monoidal r) => RightModule Natural (RngRing r)

(Abelian r, Group r) => LeftModule Integer (RngRing r)

(Abelian r, Monoidal r) => LeftModule Natural (RngRing r)

Read r => Read (RngRing r)

Show r => Show (RngRing r)

Abelian r => Abelian (RngRing r)

Abelian r => Additive (RngRing r)

(Abelian r, Monoidal r) => Monoidal (RngRing r)

Rng r => Semiring (RngRing r)

Rng r => Multiplicative (RngRing r)

(Abelian r, Group r) => Group (RngRing r)

Rng r => Unital (RngRing r)

(Rng r, Division r) => Division (RngRing r)

Rng r => Rig (RngRing r)

Rng r => Ring (RngRing r)

(Commutative r, Rng r) => Commutative (RngRing r)

Rng s => RightModule (RngRing s) (RngRing s)

Rng s => LeftModule (RngRing s) (RngRing s)

rngRingHom :: r -> RngRing r

The rng homomorphism from r to RngRing r

liftRngHom :: Ring s => (r -> s) -> RngRing r -> s

given a rng homomorphism from a rng r into a ring s, liftRngHom yields a ring homomorphism from the ring `r^` into s.