2. Let U be a ring with unity 1 and zero element 0.. (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. oll unite in A Show 1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2

2. Let U be a ring with unity 1 and zero element 0..
(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.
3. Let <A,+,> be a ring with unity and let A* be the set of all units in A. Show that the
set <A*,> is a group.
Transcribed Image Text:2. Let U be a ring with unity 1 and zero element 0.. (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. 3. Let <A,+,> be a ring with unity and let A* be the set of all units in A. Show that the set <A*,> is a group.
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