Order ideal
= Order ideal
A subset $I$ of a <partially ordered set> such that $x\in I$ and $y\le x$ imply $y\in I$. Thus membership forces all smaller elements to belong as well. This definition concerns an order, rather than an ideal of a ring.
= Order ideal
A subset $I$ of a <partially ordered set> such that $x\in I$ and $y\le x$ imply $y\in I$. Thus membership forces all smaller elements to belong as well. This definition concerns an order, rather than an ideal of a ring.