Nearring ideals, graphs and cliques

Abstract

In this paper, we dene the notion of fuzzy graph of a nearring N with respect to a level ideal t denoted by (N;;;t ). The primary aim of this notion is to depict graphically the fuzzy character which is concealed algebraically in the examples of 3-prime fuzzy ideals of a nearring N. We nd that if N is a zero-symmetric nearring and is 3prime fuzzy ideal of N, then (N;;;t ) has a special type of symmetry. We call this symmetry as the ideal symmetry of (N;;;t ). We nd the conditions under which the ideal symmetry of (N;;;t ) implies is a 3-prime fuzzy ideal of N. Finally, we obtain a result which nds all the fuzzy cliques of (N;;;t ) whenever is 3-prime and N is zerosymmetric.