AreNear-ringersAnEndageredSpecies

The number of new near-ring papers is decreasing; some people think that also the reputation of near-ring theory is shrinking. Will it be extinct in a few years? Will the last near-ringer lodge at the home of Madame Trusseaud?

I do think there is some danger in that direction. To some extent, it is also our fault, I think. Too many papers are written

• in which any paper on ring theory was taken, and each instance of "ring" was changed into "near-ring" (with slight modifications), or
• which study strongly weakly semi-half-quasi-infra-delta-almost near-rings which are 9-primary, constant, without nilpotent elements, and without anything else. Often structures are considered which are unlikely to exist.

Many structures are studied without any good motivation and without having natural examples at hand. This will repel potential readers from other areas of mathematics. Instead, we should look for connections to other parts of mathematics, seek possible applications to group or ring theory, to combinatorics, number theory, or even to areas outside of algebra. Where are the white spots of near-ring theory? Here might be some:

• What about functional analysis with non-linear operators?
• Where are good results on topological near-rings, maybe concerning near-rings of continuous mappings on topological groups?
• Are there other classes of near-rings except planar ones which lead to tactical configurations or association schemes?

Do you agree? Do you have solutions and a rescue for the reputation of near-rings? Did I exaggerate like mad? Please write me, let's have a discussion---to the benefit of the structures we love most!

Guenter Pilz [Guenter.Pilz@jku.at]