Decide whether z(sqrt(-5)) unique factorization domain or not (ring theory)

emancipezN 2020-11-22 Answered
Decide whether z(5) unique factorization domain or not (ring theory)
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Expert Answer

aprovard
Answered 2020-11-23 Author has 94 answers
Step 1
To decide whether Z(5) is unique factorization domain or not.
Step 2
Note that For a integral domain R to be unique factorization domain one of the property is:
if a=p1p2p3..pn,
a=q1q2q3.qm
where p and q are irreducible in R then m=n and each pi is associative of some qj.
Step 3
Here note that 46Z[5] is an non-zero and non-unit element and 46 can be expressed as:
46=2*23, and
46=(135)(1+35)
but 2 is not associative of (135),or(1+35)
Hence, Z[5] is not unique factorization domain.
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Jeffrey Jordon
Answered 2021-11-11 Author has 2047 answers

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