2005•Algebra ColloquiumRequires access

Weakly and Strongly Regular Near-rings

Nurcan Argaç, Nico J. Groenewald

Abstract

In this paper, we prove some basic properties of left weakly regular near-rings. We give an affirmative answer to the question whether a left weakly regular near-ring with left unity and satisfying the IFP is also right weakly regular. In the last section, we use among others left 0-prime and left completely prime ideals to characterize strongly regular near-rings.

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Key concepts: Mathematics, Prime (order theory), Left and right, Von Neumann regular ring, Combinatorics, Local ring, Pure mathematics, Ring (chemistry)