Kyungpook Mathematical Journal

  • 제45권4호
  • /
  • Pages.519-526
  • /
  • 2005
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지

A Note on Potent Elements

  • Chen, Huanyin (Department of Mathematics, Zhejiang Normal University)
  • 투고 : 2003.10.13
  • 발행 : 2005.12.23
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초록

In this paper, we prove that every exchange ring can be characterized by potent elements. Also we extend [10, Theorem 3.1 and Theorem 4.1] to quasi-clean rings in which every element is a sum of a potent element and a unit.

키워드

참고문헌

  1. Comm. Algebra v.30 Commutative rings whose elements are a sum of a unit and idempotent Anderson, D.D.;Camillo, V.P.
  2. Israel J. Math. v.105 Separative cancellation for projective modules over exchange rings Ara, P.;Goodearl, K.R.;O'Meara, K.C.;Pardo, E.
  3. Structure and commutativity of associative rings;Recent Research on Pure and Applied Algebra Ashraf, M.;Pordavi, O.(ed.)
  4. Comm. Algebra v.22 Exchange rings, units and idempotents Camillo, V.P.;Yu, H.P.
  5. Algebra Represent. Theory v.2 Exchange rings with artinian primitive factors Chen, H.
  6. Comm. Algebra v.29 Units, idempotents and stable range conditions Chen, H.
  7. J. Pure Appl. Algebra v.54 Stable range one for rings with many units Goodearl, K.R.;Menal, P.
  8. Trans. Amer. Math. Soc. v.229 Lifting idempotents and exchange rings Nicholson, W.K.
  9. Comm. Algebra v.29 Extensions of clean rings Nicholson, W.K.
  10. Comm. Algebra v.31 Semiclean rings Ye, Y.