• 대한수학회보
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• 제48권3호
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• pp.611-616
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• 2011

The reflexiveness and reversibility were introduced by Mason and Cohn respectively. The structures of minimal reversible rings and minimal reflexive rings are completely determined. The term minimal means having smallest cardinality.

• 대한수학회지
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• 제51권4호
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• pp.751-771
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• 2014

We study the structure of idempotents in polynomial rings, power series rings, concentrating in the case of rings without identity. In the procedure we introduce right Insertion-of-Idempotents-Property (simply, right IIP) and right Idempotent-Reversible (simply, right IR) as generalizations of Abelian rings. It is proved that these two ring properties pass to power series rings and polynomial rings. It is also shown that ${\pi}$-regular rings are strongly ${\pi}$-regular when they are right IIP or right IR. Next the noncommutative right IR rings, right IIP rings, and Abelian rings of minimal order are completely determined up to isomorphism. These results lead to methods to construct such kinds of noncommutative rings appropriate for the situations occurred naturally in studying standard ring theoretic properties.