100%3.is not a field.EXERCISELet U be a ring with unity 1. Show thata)if 0 = 1, then U consists of only one elementb)if 0 is a unit, then U = {0}c)if U= {0}, then 0 is the unity and a unit.1.3INTEGRAL DOMAINS+In a commutative ring R a non-zero element x is called a divisor of zthere exists a non-zero element y in R such that x.y = 0.

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Answered: 3. is not a field. EXERCISE Let U be a…

Elements Of Modern Algebra

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Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 11E: 11. a. Give an example of a ring of characteristic 4, and elements in such that b. Give an...

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3. is not a field. EXERCISE Let U be a ring with unity 1. Show that a) b) c) if 0 = 1, then U consists of only one element if 0 is a unit, then U = {0} if U= {0}, then 0 is the unity and a unit.