#The product of an element of the ideal and an element of the initial ring is an element of the ideal
#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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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.
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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]].