Are there any undegrad-level examples of ring subsets which possess absorbtion property (as in ideal definition) but are not ideals (i.e. are not additive subgroups)?
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1In $2\Bbb Z$, $2\Bbb Z\setminus {2}$ – xavierm02 Oct 06 '14 at 15:37
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The union of two ideals will possess the absorption property, but not necessarily be closed under addition and subtraction. For example, in $\mathbb Z$, we have $2\mathbb Z \cup 3\mathbb Z$, which contains $2$ and $3$ but not $1=3-2$.
Dustan Levenstein
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