Difference between revisions of "Zero divisor"
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For example, in the ring of [[integer]]s taken [[modular arithmetic | modulo]] 6, 2 is a zero divisor because <math>2 \cdot 3 \equiv 0 \pmod 6</math>. However, 5 is ''not'' a zero divisor mod 6 because the only solution to the equation <math>5x \equiv 0 \pmod 6</math> is <math>x \equiv 0 \pmod 6</math>. | For example, in the ring of [[integer]]s taken [[modular arithmetic | modulo]] 6, 2 is a zero divisor because <math>2 \cdot 3 \equiv 0 \pmod 6</math>. However, 5 is ''not'' a zero divisor mod 6 because the only solution to the equation <math>5x \equiv 0 \pmod 6</math> is <math>x \equiv 0 \pmod 6</math>. | ||
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| + | 1 is not a zero divisor in any ring. | ||
A ring with no zero divisors is called an [[integral domain]]. | A ring with no zero divisors is called an [[integral domain]]. | ||
Revision as of 19:17, 19 February 2007
In a ring 
, a nonzero element 
is said to be a zero divisor if there exists a nonzero 
such that 
.
For example, in the ring of integers taken modulo 6, 2 is a zero divisor because 
. However, 5 is not a zero divisor mod 6 because the only solution to the equation 
is 
.
1 is not a zero divisor in any ring.
A ring with no zero divisors is called an integral domain.
See also
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