### 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 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Communications in Algebra*,

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

}

*Communications in Algebra*, vol. 38, no. 5, pp. 1957-1967. https://doi.org/10.1080/00927870903069645

**Graph of a nearring with respect to an ideal.** / Bhavanari, Satyanarayana; Kuncham, Syam Prasad; Kedukodi, Babushri Srinivas.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Graph of a nearring with respect to an ideal

AU - Bhavanari, Satyanarayana

AU - Kuncham, Syam Prasad

AU - Kedukodi, Babushri Srinivas

PY - 2010/5/1

Y1 - 2010/5/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77952477748&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77952477748&partnerID=8YFLogxK

U2 - 10.1080/00927870903069645

DO - 10.1080/00927870903069645

M3 - Article

VL - 38

SP - 1957

EP - 1967

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

IS - 5

ER -