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| ``Re: Additional more commonly known definition''
by jocaps on 2009-03-19 18:03:47 |
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The idea I gave on defining Partial ordering can also be defined for noncommutative ring. So I don't see why we would not do so
In your remark you defined a "positive cone", which is indeed another name for a "partial ordering" (maybe positive cone is a better name, as partial ordering are words coming from concept of "orders").
Another remark:
There is a bijection between partial orderings (positive cones) and partial order (as you original defined)
this is given by:
$P \mapsto <_P $
where P is a partial ordering, and $<_P$ is the partial order defined by
$x<_P y$ iff $y-x \in P$.
In your first remark you just gave the inverse of this bijection I defined.
jocaps |
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