find all the divisors of 0 in the ring Z_{6} of integers of modulo 6. in this system 2x3=0. so divisors of zero are 2 and 3. Again 4x3=0. So 4 is also a divisor of 0. ...... Is my approach right?
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Yes, the "zero divisors" in $\displaystyle Z_6$ are 2, 3, and 4. More generally, the zero divisors of $\displaystyle Z_n$ are the prime divisors of n and their multiples.
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