Definition:Ideal (Order Theory)/Proper Ideal
< Definition:Ideal (Order Theory)(Redirected from Definition:Proper Ideal (Order Theory))
Jump to navigation
Jump to search
Definition
Let $\struct {S, \preccurlyeq}$ be an ordered set.
Let $\II$ be an ideal on $\struct {S, \preccurlyeq}$.
Then:
- $\II$ is a proper ideal on $S$
- $\II \ne S$
That is, if and only if $\II$ is a proper subset of $S$.
Sources
There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page. |