Abstract
In this paper, we introduce the concepts of Smarandache zero divisors (S-zero divisors) and Smarandache weak zero divisors (S-weak zero divisors) in rings and we illustrate them with examples. Both S-zero divisors and S-weak zero divisors are zero divisors but all zero divisors are not S-zero divisors or S-weak zero divisors. In the ring of integers modulo n conditions have been specified on n to have S-zero divisors and S-weak zero divisors. We have proved if n is a composite number of the form or , where are distinct primes or ( p a prime with ), then z_n has S-zero divisors. Further we obtain conditions on z_nto have S-weak zero divisors, and we establish the existence of S-zero divisor if (where p an odd prime, ) or (p a prime different from 3 ) or in general, when (p,q distinct primes). We also have shown that the group ring z_2n G where n >1, has S-zero divisor and S-weak zero divisor. The group ring z_(2n+1) G, has only S-weak zero divisor.