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 . .

TY  - JOUR
AU  - Kostić, Aleksandra
AU  - Petrović, Zoran Z.
AU  - Pucanović, Zoran
AU  - Roslavcev, Maja
PY  - 2018
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/971
AB  - The conditions that allow an element of an associative, unital, not necessarily commutative ring R, to be represented as a sum of (commuting) idempotents and one nilpotent element are analyzed. Some applications to group rings are also presented.
T2  - Miskolc Mathematical Notes
T1  - A generalization of nil-clean rings
EP  - 981
IS  - 2
SP  - 969
VL  - 19
DO  - 10.18514/MMN.2018.2585
ER  - 

@article{
author = "Kostić, Aleksandra and Petrović, Zoran Z. and Pucanović, Zoran and Roslavcev, Maja",
year = "2018",
abstract = "The conditions that allow an element of an associative, unital, not necessarily commutative ring R, to be represented as a sum of (commuting) idempotents and one nilpotent element are analyzed. Some applications to group rings are also presented.",
journal = "Miskolc Mathematical Notes",
title = "A generalization of nil-clean rings",
pages = "981-969",
number = "2",
volume = "19",
doi = "10.18514/MMN.2018.2585"
}

Kostić, A., Petrović, Z. Z., Pucanović, Z.,& Roslavcev, M.. (2018). A generalization of nil-clean rings. in Miskolc Mathematical Notes, 19(2), 969-981.
https://doi.org/10.18514/MMN.2018.2585

Kostić A, Petrović ZZ, Pucanović Z, Roslavcev M. A generalization of nil-clean rings. in Miskolc Mathematical Notes. 2018;19(2):969-981.
doi:10.18514/MMN.2018.2585 .

Kostić, Aleksandra, Petrović, Zoran Z., Pucanović, Zoran, Roslavcev, Maja, "A generalization of nil-clean rings" in Miskolc Mathematical Notes, 19, no. 2 (2018):969-981,
https://doi.org/10.18514/MMN.2018.2585 . .

TY  - JOUR
AU  - Petrović, Zoran Z.
AU  - Pucanović, Zoran
PY  - 2017
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/815
AB  - To gain a better understanding of clean rings and their relatives, the clean graph of a commutative ring with identity is introduced and its various properties established. Further investigation of clean graphs leads to additional results concerning other classes of rings.
PB  - Charles Babbage Research Centre
T2  - Ars Combinatoria
T1  - The clean graph of a commutative ring
EP  - 378
SP  - 363
VL  - 134
UR  - https://hdl.handle.net/21.15107/rcub_grafar_815
ER  - 

@article{
author = "Petrović, Zoran Z. and Pucanović, Zoran",
year = "2017",
abstract = "To gain a better understanding of clean rings and their relatives, the clean graph of a commutative ring with identity is introduced and its various properties established. Further investigation of clean graphs leads to additional results concerning other classes of rings.",
publisher = "Charles Babbage Research Centre",
journal = "Ars Combinatoria",
title = "The clean graph of a commutative ring",
pages = "378-363",
volume = "134",
url = "https://hdl.handle.net/21.15107/rcub_grafar_815"
}

Petrović, Z. Z.,& Pucanović, Z.. (2017). The clean graph of a commutative ring. in Ars Combinatoria
Charles Babbage Research Centre., 134, 363-378.
https://hdl.handle.net/21.15107/rcub_grafar_815

Petrović ZZ, Pucanović Z. The clean graph of a commutative ring. in Ars Combinatoria. 2017;134:363-378.
https://hdl.handle.net/21.15107/rcub_grafar_815 .

Petrović, Zoran Z., Pucanović, Zoran, "The clean graph of a commutative ring" in Ars Combinatoria, 134 (2017):363-378,
https://hdl.handle.net/21.15107/rcub_grafar_815 .

TY  - JOUR
AU  - Petrović, Zoran Z.
AU  - Pucanović, Zoran
PY  - 2016
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/771
AB  - Let R be a commutative ring with identity and T(Gamma(R)) its total graph. The subject of this article is the investigation of the properties of the corresponding line graph L(T(Gamma(R))). The classification of all commutative rings whose line graphs are planar or toroidal is given. It is shown that for every integer g >= 0 there are only finitely many commutative rings such that gamma(L(T(Gamma(R)))) = g.
T2  - Ars Combinatoria
T1  - The line graph associated to the total graph of a commutative ring
EP  - 195
SP  - 185
VL  - 127
UR  - https://hdl.handle.net/21.15107/rcub_grafar_771
ER  - 

@article{
author = "Petrović, Zoran Z. and Pucanović, Zoran",
year = "2016",
abstract = "Let R be a commutative ring with identity and T(Gamma(R)) its total graph. The subject of this article is the investigation of the properties of the corresponding line graph L(T(Gamma(R))). The classification of all commutative rings whose line graphs are planar or toroidal is given. It is shown that for every integer g >= 0 there are only finitely many commutative rings such that gamma(L(T(Gamma(R)))) = g.",
journal = "Ars Combinatoria",
title = "The line graph associated to the total graph of a commutative ring",
pages = "195-185",
volume = "127",
url = "https://hdl.handle.net/21.15107/rcub_grafar_771"
}

Petrović, Z. Z.,& Pucanović, Z.. (2016). The line graph associated to the total graph of a commutative ring. in Ars Combinatoria, 127, 185-195.
https://hdl.handle.net/21.15107/rcub_grafar_771

Petrović ZZ, Pucanović Z. The line graph associated to the total graph of a commutative ring. in Ars Combinatoria. 2016;127:185-195.
https://hdl.handle.net/21.15107/rcub_grafar_771 .

Petrović, Zoran Z., Pucanović, Zoran, "The line graph associated to the total graph of a commutative ring" in Ars Combinatoria, 127 (2016):185-195,
https://hdl.handle.net/21.15107/rcub_grafar_771 .

TY  - JOUR
AU  - Pucanović, Zoran
AU  - Petrović, Zoran Z.
PY  - 2014
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/641
AB  - Let R be a commutative ring with identity and G(R) its intersection graph. In this paper, all toroidal graphs that are intersection graphs are classified. An improvement over the previous results concerning the planarity of these graphs is also presented.
PB  - Springer-Verlag Tokyo
T2  - Graphs and Combinatorics
T1  - Toroidality of Intersection Graphs of Ideals of Commutative Rings
EP  - 716
IS  - 3
SP  - 707
VL  - 30
DO  - 10.1007/s00373-013-1292-1
ER  - 

@article{
author = "Pucanović, Zoran and Petrović, Zoran Z.",
year = "2014",
abstract = "Let R be a commutative ring with identity and G(R) its intersection graph. In this paper, all toroidal graphs that are intersection graphs are classified. An improvement over the previous results concerning the planarity of these graphs is also presented.",
publisher = "Springer-Verlag Tokyo",
journal = "Graphs and Combinatorics",
title = "Toroidality of Intersection Graphs of Ideals of Commutative Rings",
pages = "716-707",
number = "3",
volume = "30",
doi = "10.1007/s00373-013-1292-1"
}

Pucanović, Z.,& Petrović, Z. Z.. (2014). Toroidality of Intersection Graphs of Ideals of Commutative Rings. in Graphs and Combinatorics
Springer-Verlag Tokyo., 30(3), 707-716.
https://doi.org/10.1007/s00373-013-1292-1

Pucanović Z, Petrović ZZ. Toroidality of Intersection Graphs of Ideals of Commutative Rings. in Graphs and Combinatorics. 2014;30(3):707-716.
doi:10.1007/s00373-013-1292-1 .

Pucanović, Zoran, Petrović, Zoran Z., "Toroidality of Intersection Graphs of Ideals of Commutative Rings" in Graphs and Combinatorics, 30, no. 3 (2014):707-716,
https://doi.org/10.1007/s00373-013-1292-1 . .

TY  - JOUR
AU  - Pucanović, Zoran
AU  - Petrović, Zoran Z.
PY  - 2011
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/395
AB  - We discuss the determination of the radius of the total graph of a commutative ring R in the case when this graph is connected. Typical extensions such as polynomial rings, formal power series, idealization of the R-module M and relations between the total graph of the ring R and its extensions are also dealt with.
PB  - Srpska akademija nauka i umetnosti SANU - Matematički institut, Beograd
T2  - Publications de l'Institut Mathematique
T1  - On the radius and the relation between the total graph of a commutative ring and its extensions
EP  - 9
IS  - 103
SP  - 1
VL  - 89
DO  - 10.2298/PIM1103001P
ER  - 

@article{
author = "Pucanović, Zoran and Petrović, Zoran Z.",
year = "2011",
abstract = "We discuss the determination of the radius of the total graph of a commutative ring R in the case when this graph is connected. Typical extensions such as polynomial rings, formal power series, idealization of the R-module M and relations between the total graph of the ring R and its extensions are also dealt with.",
publisher = "Srpska akademija nauka i umetnosti SANU - Matematički institut, Beograd",
journal = "Publications de l'Institut Mathematique",
title = "On the radius and the relation between the total graph of a commutative ring and its extensions",
pages = "9-1",
number = "103",
volume = "89",
doi = "10.2298/PIM1103001P"
}

Pucanović, Z.,& Petrović, Z. Z.. (2011). On the radius and the relation between the total graph of a commutative ring and its extensions. in Publications de l'Institut Mathematique
Srpska akademija nauka i umetnosti SANU - Matematički institut, Beograd., 89(103), 1-9.
https://doi.org/10.2298/PIM1103001P

Pucanović Z, Petrović ZZ. On the radius and the relation between the total graph of a commutative ring and its extensions. in Publications de l'Institut Mathematique. 2011;89(103):1-9.
doi:10.2298/PIM1103001P .

Pucanović, Zoran, Petrović, Zoran Z., "On the radius and the relation between the total graph of a commutative ring and its extensions" in Publications de l'Institut Mathematique, 89, no. 103 (2011):1-9,
https://doi.org/10.2298/PIM1103001P . .