Algerbraic Structures: Units and Zero-divisor in a Commutative Ring with Identity
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B8. Define what is meant by
(a) a unit,
(b) a zero-divisor in a commutative ring with identity.
Show that an element in a communtative ring with identity (where 1 = 0) cannot be
both a unit and a zero-divisor.
Find an element in Z...Z which is neither a unit nor a zero-divisor.
Show that... is a unit in ....
Find a unit ...
Please see the attached file for the fully formatted problems.
keywords: zero, divisors
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Solution Summary
Units and zero-divisors are investigated. The solution is detailed and well presented.
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Attachment B8
Def:
(a) A unit in a ring is an element in this ring such there exists an element in this ring and . In a word, a unit in a ring is an element with multiplicative inverse.
(b) A zero-divisor in a ring is a nonzero element in this ring, such that there exists a nonzero element in this ring and .
Proof:
Suppose is a ...
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