Zero-Divisor Graphs for Group Rings

REFERENCES

• Akbari , S. , Mohammadian , A. ( 2006 ). Zero-divisor graphs of noncommutative rings . J. Algebra 296 : 462 – 479 .
   Web of Science ®Google Scholar
• Akbari , S. , Mohammadian , A. ( 2007 ). On the zero-divisor graphs of finite rings . J. Algebra 314 : 168 – 184 .
   Web of Science ®Google Scholar
• Anderson , D. F. , Livingston , P. S. ( 1999 ). The zero-divisor graph of a commutative ring . J. Algebra 217 : 434 – 447 .
   Web of Science ®Google Scholar
• Anderson , D. F. , Mulay , S. B. ( 2007 ). On the diameter and girth of zero-divisor graph . J. Pure and Applied Algebra 210 : 543 – 550 .
   Web of Science ®Google Scholar
• Anderson , D. D. , Naseer , M. ( 1993 ). Beck's coloring of a commutative ring . J. Algebra 159 : 500 – 514 .
   Web of Science ®Google Scholar
• Axtel , M. , Coykendall , J. , Stickles , J. ( 2005 ). Zero-divisor graphs of polynomials and power series over commutative rings . Comm. Algebra 33 : 2043 – 2050 .
   Web of Science ®Google Scholar
• Beck , I. ( 1988 ). Coloring of commutative rings . J. Algebra 116 : 208 – 226 .
   Web of Science ®Google Scholar
• Lam , T. Y. ( 2001 ). A First Course in Noncommutative Rings . New York : Springer .
   Google Scholar
• Li , Y. , Bell , H. E. , Phipps , C. ( 2006 ). On reversible group rings . Bull. Aust. Math. Soc. 74 : 139 – 142 .
   Web of Science ®Google Scholar
• Li , Y. , Parmenter , M. M. ( 2007 ). Reversible group rings over commutative rings . Comm. Algebra 35 : 4096 – 4104 .
   Web of Science ®Google Scholar
• Lidl , R. , Niederreiter , H. ( 1994 ). Introduction to Finite Fields and Their Applications . Cambridge : Cambridge University Press .
   Google Scholar
• Milies , C. P. , Sehgal , S. K. ( 2002 ). An Introduction to Group Rings . Dordrecht : Kluwer Academic Publisher .
   Google Scholar
• Mulay , S. B. ( 2002 ). Cycles and symmetries of zero-divisors. Comm. Algebra 30: 3533–3558 .
   Google Scholar
• Nicholson , W. K. ( 1972 ). Local group rings . Canad. Math. Bull. 15 : 137 – 138 .
   Web of Science ®Google Scholar
• Olson , J. E. ( 1969 ). A combinatorial problem on finite abelian groups, I . J. Number Theory 1 : 8 – 10 .
   Google Scholar
• Redmond , S. ( 2012 ). The Zero-Divisor Graph of a Noncommutative Ring . Commutative Rings, 3947. Hauppauge , NY : Nova Sci. Publ .
   Google Scholar
• Communicated by S. Sehgal.
   Google Scholar