대한수학회지 (Journal of the Korean Mathematical Society)

  • 제51권4호
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  • Pages.751-771
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  • 2014
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  • 0304-9914(pISSN)
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  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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STRUCTURE OF IDEMPOTENTS IN RINGS WITHOUT IDENTITY

  • Kim, Nam Kyun (Faculty of Liberal Arts and Sciences Hanbat National University) ;
  • Lee, Yang (Department of Mathematics Education Pusan National University) ;
  • Seo, Yeonsook (Department of Mathematics Pusan National University)
  • 투고 : 2013.11.02
  • 발행 : 2014.07.01
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초록

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.

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참고문헌

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피인용 문헌

  1. Ring properties related to symmetric rings vol.24, pp.07, 2014, https://doi.org/10.1142/S0218196714500428
  2. On a property of polynomial rings over reversible rings pp.1532-4125, 2018, https://doi.org/10.1080/00927872.2018.1498865
  3. Matrix Rings over Reflexive Rings vol.25, pp.03, 2018, https://doi.org/10.1142/S1005386718000317
  4. Structure of insertion property by powers vol.28, pp.03, 2018, https://doi.org/10.1142/S0218196718500236