62.53 NilpotentElements

NilpotentElements( nr )

Let (N,+,cdot) be a near-ring with zero 0. An element n of N is called nilpotent if there is a positive integer k such that n^k = 0.

The function NilpotentElements returns a list of sublists of length 2 where the first entry is a nilpotent element n and the second entry is the smallest k such that n^k = 0.

  gap> NilpotentElements( LibraryNearring( "V4", 4 ) ); 
  [ [ (), 1 ], [ (3,4), 2 ], [ (1,2), 3 ], [ (1,2)(3,4), 3 ] ]

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