| Abstract | We give an algorithm for constructing a basis and a multiplication table of a finite-dimensional finitely-presented Lie ring. Secondly, we give relations that are equivalent to the n -Engel condition, and only have to be checked for the elements of a basis of a Lie ring. We apply this to construct the freest t -generator Lie rings that satisfy the n -Engel condition, for ( t , n ) = ( 2 , 3 ) , ( 3 , 3 ) , ( 4 , 3 ) , ( 2 , 4 ) . |
