# Tagged Questions

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### Ideals of a distributive lattice form a distributive lattice themselves

If $L$ is a distributive lattice, I need to show that the set of ideals $I(L)$ of $L$ forms a distributive lattice. Link to the question on Ideals of lattice. Ideals of Lattice. As mentioned in the ...
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### Ideals of Lattice.

If $L$ is a lattice then the ideal $I$ of $L$ is a nonempty lower segment closed under join. I need to show that the set of ideals $I(L)$ of $L$ forms a lattice under $\subseteq$ I know the ...
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### Is there a ring with the lattice of ideals isomorphic to $(\omega+1)^{\operatorname{op}}?$

In this question, I gave an example of a ring whose lattice of two-sided ideals is order-isomorphic to $\omega+1$. I've been playing a bit with trying to find rings with a given lattice of ideals ...
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### Diamonds of ideals, part 3

I'd like to wrap up the line of questioning started first in this question and then continued in this question. The only variant left to try is: "How close can you get to the Diamond lattice ...
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### Followup to “Examples of rings with ideal lattice isomorphic to $M_3$, $N_5$”

In this post: Examples of rings with ideal lattice isomorphic to $M_3$, $N_5$ a nice example was given of a non-distributive ring. The lattice of ideals turned out to be the Diamond lattice $M_3$ with ...
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### Are ideals in rings and lattices related?

There are (at least) two notions of ideals: An ideal in a ring is a set closed under addition and multiplication by arbitrary element. An ideal in a lattice is a set closed under taking smaller ...