62.42 NearringIdeals

NearringIdeals( nr )
NearringIdeals( nr, "l" )
NearringIdeals( nr, "r" )

NearringIdeals computes all (left) (right) ideals of the near-ring nr. The return value is a list of subgroups of the additive group of nr representing the according ideals. In case that nr is a transformation near-ring, FindGroup is used to determine the additive group of nr as a permutation group. If the optional parameters "l" or "r" are passed, all left resp. right ideals are computed.

  gap> n := LibraryNearring( "V4", 11 );
  LibraryNearring( "V4", 11 )
  gap> NearringIdeals( n );
  [ Subgroup( V4, [  ] ), Subgroup( V4, [ (3,4) ] ), V4 ]
  gap> NearringIdeals( n, "r" );
  [ Subgroup( V4, [  ] ), Subgroup( V4, [ (3,4) ] ), V4 ]
  gap> NearringIdeals( n, "l" );
  [ Subgroup( V4, [  ] ), Subgroup( V4, [ (3,4) ] ), 
    Subgroup( V4, [ (1,2) ] ), Subgroup( V4, [ (1,2)(3,4) ] ), V4 ]

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