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Czechoslovak Mathematical Journal

, Volume 69, Issue 1, pp 87–92 | Cite as

Note on Strongly Nil Clean Elements in Rings

  • Aleksandra KostićEmail author
  • Zoran Z. Petrović
  • Zoran S. Pucanović
  • Maja Roslavcev
Article
  • 31 Downloads

Abstract

Let R be an associative unital ring and let aR be a strongly nil clean element. We introduce a new idea for examining the properties of these elements. This approach allows us to generalize some results on nil clean and strongly nil clean rings. Also, using this technique many previous proofs can be significantly shortened. Some shorter proofs concerning nil clean elements in rings in general, and in matrix rings in particular, are presented, together with some generalizations of these results.

Keywords

nilpotent element nil clean element 

MSC 2010

13B25 15B33 16U99 

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References

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  • Aleksandra Kostić
    • 1
    Email author
  • Zoran Z. Petrović
    • 1
  • Zoran S. Pucanović
    • 2
  • Maja Roslavcev
    • 1
  1. 1.Faculty of MathematicsUniversity of BelgradeBelgradeSerbia
  2. 2.Faculty of Civil EngineeringUniversity of BelgradeBelgradeSerbia

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