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.
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U2 - 10.1080/00927870903069645
DO - 10.1080/00927870903069645
M3 - Article
AN - SCOPUS:77952477748
SN - 0092-7872
VL - 38
SP - 1957
EP - 1967
JO - Communications in Algebra
JF - Communications in Algebra
IS - 5
ER -