Tagged Questions
6
votes
1answer
67 views
Does there exist an ordered ring, with $\mathbb{Z}$ as an ordered subring, such that some ring of p-adic integers can be formed as a quotient ring?
I'm not sure if this might instead be MathOverflow material, but I'll give it a shot here first anyway.
Does any ring $R$ exist that satisfies the following properties?
$R$ is a totally ordered, ...
6
votes
1answer
118 views
Poset of idempotents
Let $A$ be an associative algebra and consider the poset $I$ of idempotents in $A$, where as usual if $e,f \in A$ we say $e \leq f$ provided that $e = fef$. Clearly $0 \in I$ is minimal, but in ...
5
votes
2answers
198 views
Why is a commutative ring with an infinite number of idempotent elements unstable?
In a book of model theory I found the following statement:
A commutative ring with an infinite number of idempotent elements unstable.
I haven't manage to prove it yet. As stability in the model ...
5
votes
2answers
231 views
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 ...
8
votes
3answers
378 views
Examples of rings with ideal lattice isomorphic to $M_3$, $N_5$
In thinking about this recent question, I was reading about distributive lattices, and the Wikipedia article includes a very interesting characterization:
A lattice is distributive if and only if ...
3
votes
1answer
112 views
Ideals and filters
The notions of a filter and an ideal on a poset make intuitive sense to me, and I can understand why they are dual:
A subset $I\subset P$ of a poset $P$ is an ideal if:
for all $x\in I$, $y\leq x$ ...
