대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제46권1호
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  • Pages.71-78
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  • 2009
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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STRONGLY CLEAN MATRIX RINGS OVER NONCOMMUTATIVE LOCAL RINGS

  • Li, Bingjun (DEPARTMENT OF MATHEMATICS AND SYSTEMS SCIENCE NATIONAL UNIVERSITY OF DEFENSE TECHNOLOGY)
  • 발행 : 2009.01.31
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⟨ 이전 논문 다음 논문 ⟩

초록

An element of a ring R with identity is called strongly clean if it is the sum of an idempotent and a unit that commute, and R is called strongly clean if every element of R is strongly clean. Let R be a noncommutative local ring, a criterion in terms of solvability of a simple quadratic equation in R is obtained for $M_2$(R) to be strongly clean.

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참고문헌

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피인용 문헌

  1. Quasipolar Property of Generalized Matrix Rings vol.42, pp.9, 2014, https://doi.org/10.1080/00927872.2013.796964
  2. ON 2 × 2 STRONGLY CLEAN MATRICES vol.50, pp.1, 2013, https://doi.org/10.4134/BKMS.2013.50.1.125
  3. Strongly Clean Matrices over Commutative Domains vol.21, pp.02, 2014, https://doi.org/10.1142/S1005386714000212
  4. Strongly clean matrices over arbitrary rings vol.399, 2014, https://doi.org/10.1016/j.jalgebra.2013.08.044
  5. StronglyJ-Clean Matrices Over Local Rings vol.40, pp.4, 2012, https://doi.org/10.1080/00927872.2010.551529
  6. PSEUDOPOLAR MATRIX RINGS OVER LOCAL RINGS vol.13, pp.03, 2014, https://doi.org/10.1142/S0219498813501090
  7. Unifying strongly clean power series rings vol.46, pp.10, 2018, https://doi.org/10.1080/00927872.2018.1444174