EXERCISE Let U be a ring with unity 1. Show that a) if 0 = 1, then U consists of only one element b) if 0 is a unit, then U = {0} c) if U = {0}, then 0 is the unity and a unit.

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EXERCISE
Let U be a ring with unity 1. Show that
a)
if 0 = 1, then U consists of only one element
b)
if 0 is a unit, then U = {0}
c)
if U = {0}, then 0 is the unity and a unit.
Transcribed Image Text:EXERCISE Let U be a ring with unity 1. Show that a) if 0 = 1, then U consists of only one element b) if 0 is a unit, then U = {0} c) if U = {0}, then 0 is the unity and a unit.
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