Ultraproducts and ultra-limits of near-rings

The construction of ultraproducts, ultrapowers and ultralimits have proven useful, both for logic and for special (algebraic) structures. It seems that these constructions might be especially useful in studying near-rings; they might provide solutions to long-standing problems. Among other results, we show that ultraproducts of primitive near rings are again primitive.Part of this work was done while the second author was a Visiting Professor at the University of Southwestern Louisiana (Lafayette, La). This author expresses his gratitude for the received hospitality and for most valuable discussions at this Department. Special thanks are due to Professors D. Blumberg, H. Heatherly and A. Iskander.