Smarandache-Zero Divisors in Group Rings

نویسنده

  • W. B. Vasantha
چکیده

The study of zero-divisors in group rings had become interesting problem since 1940 with the famous zero-divisor conjecture proposed by G.Higman [2]. Since then several researchers [1, 2, 3] have given partial solutions to this conjecture. Till date the problem remains unsolved. Now we introduce the notions of Smarandache zero divisors (S-zero divisors) and Smarandache week zero divisors (S-weak zero divisors) in group rings and study them. Both S-zero divisors and Sweak zero divisors are zero divisors but all zero divisors are not S-zero divisors or S-weak zero divisors. Even here we can modify the zero divisor conjecture and suggest the S-zero divisor conjecture and S-weak zero divisor conjecture for group rings. Thus the study has its own importance. Unlike in case of group rings of finite groups over field of characteristic zero where one is always gurranteed the zero divisors, we can not establish the same in case of S-zero divisors or S-weak zero divisors.

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تاریخ انتشار 2005