Geodesic
Note on strongly nil clean elements in rings
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 87-92 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/CMJ.2018.0167-17
Classification : 13B25, 15B33, 16U99
Keywords: nilpotent element; nil clean element 
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     author = {Kosti\'c, Aleksandra and Petrovi\'c, Zoran Z. and Pucanovi\'c, Zoran S. and Roslavcev, Maja},
     title = {Note on strongly nil clean elements in rings},
     journal = {Czechoslovak Mathematical Journal},
     pages = {87--92},
     year = {2019},
     volume = {69},
     number = {1},
     doi = {10.21136/CMJ.2018.0167-17},
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     zbl = {07088771},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2018.0167-17/}
}
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Kostić, Aleksandra; Petrović, Zoran Z.; Pucanović, Zoran S.; Roslavcev, Maja. Note on strongly nil clean elements in rings. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 87-92. doi: 10.21136/CMJ.2018.0167-17

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