• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1957-1972
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• 2013

The reflexive property for ideals was introduced by Mason and has important roles in noncommutative ring theory. In this note we study the structure of idempotents satisfying the reflexive property and introduce reflexive-idempotents-property (simply, RIP) as a generalization. It is proved that the RIP can go up to polynomial rings, power series rings, and Dorroh extensions. The structure of non-Abelian RIP rings of minimal order (with or without identity) is completely investigated.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.675-677
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• 2018

• Proceedings of the Korean Society of Crop Science Conference
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• 2006.04a
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• pp.306-307
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• 2006

• Proceedings of the Korean Society of Crop Science Conference
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• 2006.04a
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• pp.238-239
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• 2006

• Korean Journal of Mathematics
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• v.21 no.1
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• pp.41-53
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• 2013

Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, introducing the notion of nil-Armendariz rings. Hizem extended the nil-Armendariz property for polynomial rings onto power-series rings, say nil power-serieswise rings. In this paper, we introduce the notion of power-serieswise CN rings that is a generalization of nil power-serieswise Armendariz rings. Finally, we study the nil-Armendariz property for Ore extensions and skew power series rings.

• Proceedings of the Korean Society of Crop Science Conference
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• 2005.08a
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• pp.142-143
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• 2005

• The Bulletin of The Korean Astronomical Society
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• v.24 no.1
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• pp.50-50
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• 1999

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 2004.11a
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• pp.188-188
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• 2004

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 2004.11a
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• pp.162-162
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• 2004

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.461-472
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• 2021

We study a new ring property called axis-commutativity. Axis-commutative rings are seated between commutative rings and duo rings and are a generalization of division rings. We investigate the basic structure and several extensions of axis-commutative rings.