# Category:Prime Ideals (Order Theory)

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This category contains results about **Prime Ideals (Order Theory)** in the context of **Order Theory**.

Let $I$ be an ideal in an ordered set $S$.

Then $I$ is a **prime ideal** in $S$ if and only if $S \setminus I$ is a filter.

## Also see

## Pages in category "Prime Ideals (Order Theory)"

The following 13 pages are in this category, out of 13 total.

### C

### F

### I

- If Element Does Not Belong to Ideal then There Exists Prime Ideal Including Ideal and Excluding Element
- If Ideal and Filter are Disjoint then There Exists Prime Filter Including Filter and Disjoint from Ideal
- If Ideal and Filter are Disjoint then There Exists Prime Ideal Including Ideal and Disjoint from Filter