대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제60권5호
  • /
  • Pages.1321-1334
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  • 2023
  • /
  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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STRUCTURE OF IDEMPOTENTS IN POLYNOMIAL RINGS AND MATRIX RINGS

  • Juan Huang (Department of Mathematics Pusan National University) ;
  • Tai Keun Kwak (Department of Data Science Daejin University) ;
  • Yang Lee (Department of Mathematics Yanbian University and Institute for Applied Mathematics and Optics Hanbat National University) ;
  • Zhelin Piao (Department of Mathematics Yanbian University)
  • 투고 : 2022.10.04
  • 심사 : 2023.06.09
  • 발행 : 2023.09.30
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초록

An idempotent e of a ring R is called right (resp., left) semicentral if er = ere (resp., re = ere) for any r ∈ R, and an idempotent e of R∖{0, 1} will be called right (resp., left) quasicentral provided that for any r ∈ R, there exists an idempotent f = f(e, r) ∈ R∖{0, 1} such that er = erf (resp., re = fre). We show the whole shapes of idempotents and right (left) semicentral idempotents of upper triangular matrix rings and polynomial rings. We next prove that every nontrivial idempotent of the n by n full matrix ring over a principal ideal domain is right and left quasicentral and, applying this result, we can find many right (left) quasicentral idempotents but not right (left) semicentral.

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과제정보

The fourth named author was supported by the Science and Technology Research Project of Education Department of Jilin Province, China(JJKH20210563KJ).

참고문헌

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