C. J. Maxson (Texas A & M Univ.) recently reported the following problem: Consider the nearring , and let . Is A a maximal right ideal? Here, already rather straightforward methods for dealing with this infinite nearring should help.
Another problem is to determine nearrings generated by only one element, or, conversely, find the generator of a nearring that can be generated by one element but is given differently. This problem (posed by P. Fuchs) arises in the context of fractal geometry and in non-linear systems design.
To get a more complete version of , it is necessary to find out as many situations as possible in which small nearrings arise. For example, a small but rather unknown nearring can be a nice centralizer nearring (, ), or could be better understood as a matrix nearring ().