Graph of a Nearring with Respect to an Ideal |
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| Authors: | Satyanarayana Bhavanari Syam Prasad Kuncham |
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| Affiliation: | 1. Department of Mathematics , Acharya Nagarjuna University , Nagarjuna Nagar, Andhra Pradesh, India;2. Department of Mathematics, Manipal Institute of Technology , Manipal University , Manipal, Karnataka, India |
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| Abstract: | We introduce a concept called the graph of a nearring N with respect to an ideal I of N denoted by G I (N). Then we define a new type of symmetry called ideal symmetry of G I (N). The ideal symmetry of G I (N) implies the symmetry determined by the automorphism group of G I (N). We prove that if I is a 3-prime ideal of a zero-symmetric nearring N then G I (N) is ideal symmetric. Under certain conditions, we find that if G I (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. |
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| Keywords: | Graph Ideal Nearring |
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