Given an element x in an noncommutative ring, isLeftRegular returns true if a*x=0 implies a=0 for all a in the specified homogeneous degree n. Likewise isRightRegular returns true if x*a=0 implies a=0 for all elements a of degree n. The method calls leftMultiplicationMap or rightMultiplicationMap as appropriate and checks the kernel in the specified degree.
i1 : B = threeDimSklyanin(QQ,{1,1,-1},{x,y,z}) o1 = B o1 : FreeAlgebraQuotient |
i2 : g = z^3 + y*z*x - z*y*x - y^3 3 3 o2 = - y + y*z*x - z*y*x + z o2 : B |
i3 : isLeftRegular(g,6) o3 = true |
i4 : C = QQ<|x,y|> o4 = C o4 : FreeAlgebra |
i5 : D = C/ideal{x^2+x*y,y^2} o5 = D o5 : FreeAlgebraQuotient |
i6 : isLeftRegular(x,1) o6 = true |
i7 : isRightRegular(x,1) o7 = false |
The object isLeftRegular is a method function.