### Abstract

We introduce a concept called the graph of a nearring N with respect to an ideal I of N denoted by G_{1}(N) Then we define a new type of symmetry called ideal symmetry of G_{1}(N). The ideal symmetry of G_{1}(N) implies the symmetry determined by the automorphism group of G_{1}(N) We prove that if I is a 3-prime ideal of a zero-symmetric nearring N then G_{1}(N) is ideal symmetric. Under certain conditions, we find that if G_{1}(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.

Original language | English |
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Pages (from-to) | 1957-1967 |

Number of pages | 11 |

Journal | Communications in Algebra |

Volume | 38 |

Issue number | 5 |

DOIs | |

Publication status | Published - 01-05-2010 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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## Cite this

Bhavanari, S., Kuncham, S. P., & Kedukodi, B. S. (2010). Graph of a nearring with respect to an ideal.

*Communications in Algebra*,*38*(5), 1957-1967. https://doi.org/10.1080/00927870903069645