I know this sounds like a basic question but I'm really confused. What does the notation $\langle x,3\rangle$ refer to for $\mathbb Z[x]$? Can someone write out what this is?
What does $\langle x,3\rangle$ mean if I'm talking about $\mathbb Z[x]$
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abstract-algebra
notation
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1It's a mystery. – 2011-05-13
2 Answers
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$\rm \langle x,3\rangle\:$ could mean a few things. Here are some possibilities, listed most-likely first. It could denote the ideal $\rm\: x\ \mathbb Z[x] + 3\ \mathbb Z[x]\:.\:$ Or it could denote the additive subgroup $\rm\:x\ \mathbb Z + 3\ \mathbb Z\:.\:$ Finally it could denote $\rm\:gcd(x,3)\:,\:$ though the gcd is more commonly denoted as $\rm\:(x,3)\:$ or $\rm\:[x,3]\:.$