Graph of a nearring with respect to an ideal

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14 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 languageEnglish
Pages (from-to)1957-1967
Number of pages11
JournalCommunications in Algebra
Volume38
Issue number5
DOIs
Publication statusPublished - 01-05-2010

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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