Question

Show that every nonzero element of zn is a unit or a zero-divisor

Answer 1

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$<b>$Now we show that in any finite commutative ring with 1, call it R, a non-invertible element a = 0 is a zero divisor. (This applies then in particular to Zn.) Namely assume a does not have an inverse and consider the function f : R → R, x ↦→ ax.

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Answer 2

Answer:

Now we show that in any finite commutative ring with 1, call it R, a non-invertible element a = 0 is a zero divisor. (This applies then in particular to Zn.) Namely assume a does not have an inverse and consider the function f : R → R, x ↦→ ax.

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