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AssociativeAlgebras :: isNormal(RingElement)

isNormal(RingElement) -- Determines if an element of a noncommutatie ring is normal

Synopsis

Description

Given an element x in a noncommutative ring R, this method returns true if Rx=xR.

i1 : A = QQ<|a,b,c|>

o1 = A

o1 : FreeAlgebra
i2 : I = ideal {a*b+b*a,a*c+c*a,b*c+c*b}

o2 = ideal (a*b + b*a, a*c + c*a, b*c + c*b)

o2 : Ideal of A
i3 : B = A/I

o3 = B

o3 : FreeAlgebraQuotient
i4 : sigma = map(B,B,{b,c,a})

o4 = map (B, B, {b, c, a})

o4 : RingMap B <--- B
i5 : C = oreExtension(B,sigma,w)

o5 = C

o5 : FreeAlgebraQuotient
i6 : isCentral w

o6 = false
i7 : isNormal w

o7 = true

See also