Note on Strongly Nil Clean Elements in Rings
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.
Keywords:
nilpotent element / nil clean elementSource:
Czechoslovak Mathematical Journal, 2019, 69, 1, 87-92Publisher:
- Springer New York LLC
Funding / projects:
- Analysis and algebra with applications (RS-174032)
DOI: 10.21136/CMJ.2018.0167-17
ISSN: 0011-4642
WoS: 000461365800008
Scopus: 2-s2.0-85051439095
Collections
Institution/Community
GraFarTY - 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 . .