We introduce a concept called the graph of a nearring N with respect to an ideal I of N denoted by G1(N) Then we define a new type of symmetry called ideal symmetry of G1(N). The ideal symmetry of G1(N) implies the symmetry determined by the automorphism group of G1(N) We prove that if I is a 3-prime ideal of a zero-symmetric nearring N then G1(N) is ideal symmetric. Under certain conditions, we find that if G1(N) is ideal symmetric then I is 3-prime. Finally, we deduce that if N is an equiprime nearring then the prime graph of N is ideal symmetric.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory