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From An Introduction to Abstract Algebra by T. Hungerford

Section 3.2 #29

Let R be a ring with identity and no zero divisors.

If ab is a unit in R prove that a and b are units.

2. Relevant equations

c is a unit in R if and only if there exists an element x in R s.t. cx=xc=1

where 1 is the identity element of R.

c is a zero divisor in R if and only if 1)c is not equal to 0 and 2)there exists

and element d in R s.t. either cd=0 or dc=0.

3. The attempt at a solution

Any help please? Thank you.

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# Abstract Algebra: Unit question I am stumped!

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