Nearring ideals, graphs and cliques

Abstract

In this paper, we define the notion of fuzzy graph of a nearring N with respect to a level ideal µ t denoted by (N, µ, σ, 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 find that if N is a zero-symmetric nearring and µ is 3-prime fuzzy ideal of N , then (N, µ, σ, t) has a special type of symmetry. We call this symmetry as the ideal symmetry of (N, µ, σ, t). We find the conditions under which the ideal symmetry of (N, µ, σ, t) implies µ is a 3-prime fuzzy ideal of N . Finally, we obtain a result which finds all the fuzzy cliques of (N, µ, σ, t) whenever µ is 3-prime and N is zerosymmetric.Mathematics Subject Classification: 16Y30, 03E72, 16Y99