62.43 InvariantSubnearrings

InvariantSubnearrings( nr )

A subnear-ring (M,+,cdot) of a near-ring (N,+,cdot) is called an invariant subnear-ring if both, M cdot N subseteq M and N cdot M subseteq M.

The function InvariantSubnearrings computes all invariant subnear-rings of the near-ring nr. The function returns a list of near-rings representing the according invariant subnear-rings. In case that nr is a transformation near-ring, FindGroup is used to determine the additive group of nr as a permutation group.

  gap> InvariantSubnearrings( LibraryNearring( "V4", 22 ) );
  [ Nearring( Subgroup( V4, [ (1,2) ] ), function ( x, y )
          return elms[tfle.(f[Position( elms, y )])[Position( elms, x )]
             ];
      end ), Nearring( V4, function ( x, y )
          return elms[tfle.(f[Position( elms, y )])[Position( elms, x )]
             ];
      end ) ]

Previous Up Top Next
Index