algebra-2.0.2: Constructive abstract algebra

Numeric.Ring.Rng

Synopsis

# Documentation

data RngRing r Source

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 rSource

The rng homomorphism from r to RngRing r

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

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