Subject to certain faithfulness requirements in a morita context for near-rings, a canonical representation thereof is provided. Necessary and sufficient conditions (using an idempotent element) on a near-ring are given which determine when the nearring is a morita near-ring.
"Representation of near-ring Morita contexts and recognizing Morita near-rings." Tsukuba J. Math. 20 (1) 107 - 113, June 1996. https://doi.org/10.21099/tkbjm/1496162981