Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 69, No. 1, pp. 87-92, 2019

Note on strongly nil clean elements in rings

Aleksandra Kostić, Zoran Z. Petrović, Zoran S. Pucanović, Maja Roslavcev

Received April 10, 2017. Published online June 22, 2018.

Abstract: Let $R$ be an associative unital ring and let $a\in R$ 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

Classification MSC: 13B25, 15B33, 16U99

DOI: 10.21136/CMJ.2018.0167-17

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Aleksandra Kostić, Zoran Z. Petrović, Maja Roslavcev, Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Belgrade, Serbia, e-mail: alex@matf.bg.ac.rs, zoranp@matf.bg.ac.rs, roslavcev@matf.bg.ac.rs; Zoran S. Pucanović, Faculty of Civil Engineering, University of Belgrade, Bulevar kralja Aleksandra 73, 11000 Belgrade, Serbia, e-mail: pucanovic@grf.bg.ac.rs

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