# ncKernel -- Compute the graph ideal of a ring map between noncommutative rings.

## Synopsis

• Usage:
I = ncKernel f
• Inputs:
• f, ,
• Optional inputs:
• DegreeLimit => ..., default value 10
• Strategy => ..., default value "F4"
• Outputs:

## Description

This function computes (a Groebner basis of) the kernel of a ring map between noncommutative rings.

 i1 : A = QQ<|a,b,c|> o1 = A o1 : FreeAlgebra i2 : B = QQ<|x,y|> o2 = B o2 : FreeAlgebra i3 : f = map(B,A,{x*y*x,y*x*y,x*y}) o3 = map (B, A, {x*y*x, y*x*y, x*y}) o3 : RingMap B <--- A i4 : K = ncKernel f Warning: Parallel F4 Algorithm not available over current coefficient ring. Converting to Naive algorithm. o4 = ideal 0 o4 : Ideal of A

The generators returned by this function are in fact a Groebner basis of the kernel, so it may not be a minimal generating set.

The DegreeLimit and Strategy options are forwarded on to the call to the Groebner basis routine NCGB.

## Ways to use ncKernel :

• "ncKernel(RingMap)"

## For the programmer

The object ncKernel is .