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Let n be a positive integer. Consider the ring R= Z/nZ. Let a E R. Show that a is either a unit (i.e., a has an inverse) or a zero divisor.

Let n be a positive integer. Consider the ring R= Z/nZ. Let a E R. Show that a is either a unit (i.e., a has an inverse) or a zero divisor.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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abstract algebra

**Problem 9:** Let \( n \) be a positive integer. Consider the ring \( R = \mathbb{Z}/n\mathbb{Z} \). Let \( a \in R \). Show that \( a \) is either a unit (i.e., \( a \) has an inverse) or a zero divisor.
Transcribed Image Text:**Problem 9:** Let \( n \) be a positive integer. Consider the ring \( R = \mathbb{Z}/n\mathbb{Z} \). Let \( a \in R \). Show that \( a \) is either a unit (i.e., \( a \) has an inverse) or a zero divisor.
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