Difference between revisions of "Ideal (mathematics)"

Revision as of 17:59, March 21, 2009

In ring theory, an ideal is defined as a subset of a ring with the following properties:

Zero is an element of the ideal
The ideal is closed under addition
The product of an element of the ideal and an element of the initial ring is an element of the ideal

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 #The ideal is closed under addition
 #The product of an element of the ideal and an element of the initial ring is an element of the ideal
-In common usage, an ideal is that which sought after as being the answer that is desired whether it be an object, a frame of mind, a condition, etc.
-When someone is called an '''idealist''', it often means that they are more concerned with goals that have not yet been attained than the current situation. The term can also be used to denote someone as an [[optimist]]. For an antonym of idealist, see [[realist]].
 [[Category:Mathematics]]