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Suppose $P$ is the set of all subsets of a set $X$ and $P$ is a ring. Let $p$ be an element in $P$ (so that $p$ is a subset of $X$). What does it mean to say "an ideal generated by $p$"? And suppose there is some $q\in P$ then what does it mean to say "an ideal generated by (p,q)"? 

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    Usually sets don't have ideals... are you talking about rings?2012-02-15
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    @Ted: The set of all subsets of set X forms a ring, you are right.2012-02-15
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    Or are you talking about ideals in the [order-theoretic sense](http://en.wikipedia.org/wiki/Ideal_%28order_theory%29), viewing $P$ as a partially ordered set under inclusion?2012-02-15
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    @ArturoMagidin: I am not familiar with the entity you have described, so I guess it isn't that. I have edited the question. P is supposed to be a ring.2012-02-15
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    @eugene If you give a reference to the text that you seek to comprehend, then we can use this to help supply an optimal answer. Lacking such, we are forced to guess the context, which may result in non-optimal replies.2012-02-15

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