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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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abstract algebra

e1 definnd
a fing
omor-
9. 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.
10. LA
lemeur
nilpotent if an = 0 for some
Transcribed Image Text:e1 definnd a fing omor- 9. 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. 10. LA lemeur nilpotent if an = 0 for some
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