# Graph of a nearring with respect to an ideal

Research output: Contribution to journalArticle

11 Citations (Scopus)

### Abstract

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.

Original language English 1957-1967 11 Communications in Algebra 38 5 https://doi.org/10.1080/00927870903069645 Published - 01-05-2010

### Fingerprint

Near-ring
Graph in graph theory
Symmetry
Prime Graph
Prime Ideal
Automorphism Group
Deduce
Imply
Zero

### All Science Journal Classification (ASJC) codes

• Algebra and Number Theory

### Cite this

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

In: Communications in Algebra, Vol. 38, No. 5, 01.05.2010, p. 1957-1967.

Research output: Contribution to journalArticle

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