Algebra.Ring.Noetherian

Documentation

class (Commutative r, Ring r) => NoetherianRing r

Instances

NoetherianRing Int

NoetherianRing Integer

Integral n => NoetherianRing (Ratio n)

(Commutative (Complex r), Ring (Complex r)) => NoetherianRing (Complex r)

(Commutative (Complex r), Ring (Complex r)) => NoetherianRing (Complex r)

(Eq r, NoetherianRing r) => NoetherianRing (Polynomial r)

(IsOrder order, IsPolynomial Nat r n) => NoetherianRing (OrderedPolynomial r order n)

By Hilbert's finite basis theorem, a polynomial ring over a noetherian ring is also a noetherian ring.

data Ideal r

Constructors

forall n . Ideal (Vector r n)

Instances

(NoetherianRing r, Eq r, IsMonomialOrder ord) => Monomorphicable Nat (:.: * Nat Ideal (OrderedPolynomial r ord))

Eq r => Eq (Ideal r)

Ord r => Ord (Ideal r)

Show r => Show (Ideal r)

addToIdeal :: r -> Ideal r -> Ideal r

toIdeal :: NoetherianRing r => [r] -> Ideal r

appendIdeal :: Ideal r -> Ideal r -> Ideal r

generators :: Ideal r -> [r]

filterIdeal :: NoetherianRing r => (r -> Bool) -> Ideal r -> Ideal r

mapIdeal :: (r -> r') -> Ideal r -> Ideal r'

principalIdeal :: r -> Ideal r