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NCAlgebra :: isNormal(NCRingElement)

isNormal(NCRingElement) -- Determines if a given NCRingElement is normal

Synopsis

Description

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

i1 : A = QQ{a,b,c}

o1 = A

o1 : NCPolynomialRing
i2 : I = ncIdeal {a*b+b*a,a*c+c*a,b*c+c*b}

o2 = Two-sided ideal {ba+ab, ca+ac, cb+bc}

o2 : NCIdeal
i3 : B = A/I
--Calling Bergman for NCGB calculation.
Complete!

o3 = B

o3 : NCQuotientRing
i4 : sigma = ncMap(B,B,{b,c,a})

o4 = NCRingMap B <--- B

o4 : NCRingMap
i5 : isWellDefined sigma

o5 = true
i6 : C = oreExtension(B,sigma,w)
--Calling Bergman for NCGB calculation.
Complete!

o6 = C

o6 : NCQuotientRing
i7 : isCentral w

o7 = false
i8 : isNormal w

o8 = true

See also

Ways to use this method: