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Pick out the correct statements from the following list:

a. A homomorphic image of a UFD (unique factorization domain) is again a UFD.

b. The element $2 \in \mathbb Z[\sqrt{−5}]$ is irreducible in $\mathbb Z[\sqrt{−5}]$.

c. Units of the ring $\mathbb Z[\sqrt{−5}]$ are the units of $\mathbb Z$.

d. The element $2$ is a prime element in $\mathbb Z[\sqrt{−5}]$.

Ian Coley
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ARIJIT PAL
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  • What are your thoughts ? Any guess ? – Joel Cohen May 28 '13 at 05:00
  • Since you are new, I want to give some advice about the site: To get the best possible answers, you should explain what your thoughts on the problem are so far. That way, people won't tell you things you already know, and they can write answers at an appropriate level; also, people tend to be more willing to help you if you show that you've tried the problem yourself. Also, many would consider your post rude because it is a command ("Pick"), not a request for help, so please consider rewriting it. – Zev Chonoles May 28 '13 at 05:00
  • Please see here for how to typeset common math expressions with LaTeX, and see here for how to use Markdown formatting. – Zev Chonoles May 28 '13 at 05:01
  • my confusion arises between b and d.. – ARIJIT PAL May 28 '13 at 05:06
  • @ARIJITPAL: Have you looked at the wikipedia articles on irreducible elements and prime elements? Do you understand that they are not the same concept? – Zev Chonoles May 28 '13 at 05:09
  • @ZevChonoles you are absolutely correct that am new in that site..and thanks for the advice .. – ARIJIT PAL May 28 '13 at 05:10
  • same:http://math.stackexchange.com/questions/221527/some-question-related-to-mathbbz-sqrt-5-and-ufd?rq=1 – jim May 28 '13 at 05:24

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