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Results tagged with posets
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user 88133
A poset or partially ordered set is a set endowed with a partial order, meaning a binary relation $\leq$ which is reflexive ($x \leq x$ for all $x$), antisymmetric ($x\leq y$ and $y\leq x$ implies $x=y$), and transitive ($x\leq y$ and $y\leq z$ implies $x \leq z$).
11
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0
answers
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Poset of nonvanishing minors of a matrix
What posets can be realized in this way? Does it depend on the field? What if we restrict to integer $0$-$1$ matrices? …
- 6,237
6
votes
Zorn's lemma: old friend or historical relic?
Here's another example, from a rather worm's-eye view. (Apologies for too many edits.)
Theorem: Let $R$ be a non-zero commutative ring with $1$.
Then there exists a minimal prime ideal in $R$, i.e., a …
- 6,237