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.