62.65 IsPlanarNearring

IsPlanarNearring( nr )

Let (N,+,cdot) be a right near-ring. For a,b in N define the equivalence relation equiv by a equiv b: Leftrightarrow forall n in N: ncdot a = ncdot b. If a equiv b then a and b are called equivalent multipliers. A near-ring N is called planar if mid N/_{equiv} mid ge 3 and if every equation of the form xcdot a = xcdot b + c has a unique solution for two non equivalent multipliers a and b.

The function IsPlanarNearring returns the according value true or false for a near-ring nr.

Remark: this function works only for library near-rings, i.e. near-rings which are constructed by using the function LibraryNearring.

  gap> IsPlanarNearring( LibraryNearring( "V4", 22 ) );
  false

Previous Up Top Next
Index