oreIdeal -- Creates the defining ideal of an Ore extension of a noncommutative ring

Synopsis

Usage:

oreIdeal(A,sigma,delta,x) or oreIdeal(A,sigma,x)
Inputs:
- A, an instance of the type NCRing,
- sigma, an instance of the type NCRingMap,
- delta, an instance of the type NCRingMap,
- x, an instance of the type NCRingElement, or a Symbol
Optional inputs:
- Degree (missing documentation) => ..., default value 1,
Outputs:
- an instance of the type NCIdeal,

Description

Given a ring A, an Ore extension of A by x is the quotient of the free extension A<x> by the relations x*a - sigma(a)*x-delta(a) where sigma is an automorphism of A and delta is a sigma-derivation. This method returns the defining ideal (in the appropriate tensor algebra) of an Ore extension of A by x. The current version assumes the sigma-derivation delta is 0.

i1 : B = skewPolynomialRing(QQ,(-1)_QQ,{x,y,z,w})
--Calling Bergman for NCGB calculation.
Complete!

o1 = B

o1 : NCQuotientRing

i2 : sigma = ncMap(B,B,{y,z,w,x})

o2 = NCRingMap B <--- B

o2 : NCRingMap

i3 : C = oreIdeal(B,sigma,a)

o3 = Two-sided ideal {yx+xy, zx+xz, zy+yz, wx+xw, wy+yw, wz+zw, ax-ya, ay-za, az-wa, aw-xa}

o3 : NCIdeal

Ways to use oreIdeal :

oreIdeal(NCRing,NCRingMap,NCRingElement)
oreIdeal(NCRing,NCRingMap,NCRingMap,NCRingElement)
oreIdeal(NCRing,NCRingMap,NCRingMap,Symbol)
oreIdeal(NCRing,NCRingMap,Symbol)

For the programmer

The object oreIdeal is a method function with options.

oreIdeal -- Creates the defining ideal of an Ore extension of a noncommutative ring

Synopsis

Description

See also

Ways to use oreIdeal :

For the programmer