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![[parent]](http://images.planetmath.org:8080/images/uparrow.png) Viewing Correction to 'prime ideal'
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non-commutative version by antizeus
Correction id: 41
Filed on: 2001-10-20 02:10:40
Status: Accepted on 2001-10-20 14:27:43
Type: Addendum
Correction text:
A (two-sided) ideal P of a ring R is called a prime ideal if the following equivalent conditions are met:
(a) If I and J are left ideals with IJ \subset P, then I \subset P or J \subset P.
(b) If I and J are right ideals with IJ \subset P, then I \subset P or J \subset P.(c) If I and J are two-sided ideals with IJ \subset P, then I \subset P or J \subset P.(d) If x and y are elements of R with xRy \subset P, then x \in P or y \in P.
(e) R/P is a prime ring. |
No comment from object owner djao.
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