Ideal

Principal ideal

A (left/right/two-sided) ideal is called principal iff it is generated by a single element. ring Specifically, is a

• left principal ideal iff for some ;
• right principal ideal iff for some ;
• two-sided principal ideal iff for some .

A ring in which every ideal is (left/right/two-sided) principal is called a (left/right/two-sided) principal ideal ring.

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