Subsections

• Related Structures
• Numerical Invariants
• Ring Predicates and Booleans

Category(R) : RngIntRes -> Cat

Parent(R) : RngIntRes -> PowerStructure

PrimeRing(R) : RngIntRes -> RngIntRes

Center(R) : RngIntRes -> RngIntRes

Given R=Z/mZ, create the abelian group of integers modulo m under addition. This returns the finite additive abelian group A (of order m) together with a map from the ring Z/mZ to A, sending 1 to 1.

UnitGroup(R) : RngIntRes -> GrpAb, Map

Given R=Z/mZ, create the multiplicative group of R as an abelian group. This returns an (additive) abelian group A of order phi(m), together with a map from R to A, sending a primitive root of R to 1.

Given R, the ring of integers modulo m or an ideal of it, and an element n of R, create the ideal aZintersect Z of the ring of integers. Note that this creates an ideal, not just a subring.

Create the enumerated set consisting of the elements of the residue class ring R.

Characteristic(R) : RngIntRes -> RngIntResElt

# R : RngIntRes -> RngIntResElt

Given a residue class ring R=Z/mZ, this function returns the common modulus m for the elements of R.

Given a residue class ring R=Z/mZ, this function returns the factorization of the common modulus m for the elements of R.

IsCommutative(R) : RngIntRes -> BoolElt

IsUnitary(R) : RngIntRes -> BoolElt

IsFinite(R) : RngIntRes -> BoolElt

IsOrdered(R) : RngIntRes -> BoolElt

IsField(R) : RngIntRes -> BoolElt

IsEuclideanDomain(R) : RngIntRes -> BoolElt

IsPID(R) : RngIntRes -> BoolElt

IsUFD(R) : RngIntRes -> BoolElt

IsDivisionRing(R) : RngIntRes -> BoolElt

IsEuclideanRing(R) : RngIntRes -> BoolElt

IsPrincipalIdealRing(R) : RngIntRes -> BoolElt

IsDomain(R) : RngIntRes -> BoolElt

R eq R : RngIntRes, Rng -> BoolElt

R ne R : RngIntRes, Rng -> BoolElt