Let R be an associative unital ring and let a 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.
TY - JOUR
AU - Kostić, Aleksandra
AU - Petrović, Zoran Z.
AU - Pucanović, Zoran
AU - Roslavcev, Maja
PY - 2019
UR - https://grafar.grf.bg.ac.rs/handle/123456789/997
AB - Let R be an associative unital ring and let a 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.
PB - Springer New York LLC
T2 - Czechoslovak Mathematical Journal
T1 - Note on Strongly Nil Clean Elements in Rings
EP - 92
IS - 1
SP - 87
VL - 69
DO - 10.21136/CMJ.2018.0167-17
ER -
@article{
author = "Kostić, Aleksandra and Petrović, Zoran Z. and Pucanović, Zoran and Roslavcev, Maja",
year = "2019",
abstract = "Let R be an associative unital ring and let a 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.",
publisher = "Springer New York LLC",
journal = "Czechoslovak Mathematical Journal",
title = "Note on Strongly Nil Clean Elements in Rings",
pages = "92-87",
number = "1",
volume = "69",
doi = "10.21136/CMJ.2018.0167-17"
}
Kostić, A., Petrović, Z. Z., Pucanović, Z.,& Roslavcev, M.. (2019). Note on Strongly Nil Clean Elements in Rings. in Czechoslovak Mathematical Journal
Springer New York LLC., 69(1), 87-92.
https://doi.org/10.21136/CMJ.2018.0167-17
Kostić A, Petrović ZZ, Pucanović Z, Roslavcev M. Note on Strongly Nil Clean Elements in Rings. in Czechoslovak Mathematical Journal. 2019;69(1):87-92.
doi:10.21136/CMJ.2018.0167-17 .
Kostić, Aleksandra, Petrović, Zoran Z., Pucanović, Zoran, Roslavcev, Maja, "Note on Strongly Nil Clean Elements in Rings" in Czechoslovak Mathematical Journal, 69, no. 1 (2019):87-92,
https://doi.org/10.21136/CMJ.2018.0167-17 . .
