236
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

On graded nil clean rings

&
Pages 4079-4089 | Received 09 Sep 2017, Published online: 01 Mar 2018

References

  • Anderson, F. W., Fuller, K. R. (1992). Rings and Categories of Modules. Berlin/Heidelberg/New York: Springer.
  • Breaz, S., Călugăreanu, G., Danchev, P., Micu, T. (2013). Nil-clean matrix rings. Linear Algebra Appl. 439:3115–3119.
  • Chadeyras, M. (1970). Essai d’une théorie noetherienne pour les anneaux commutatifs, dont la graduation est aussi générale que possible. Mémoire de la Société Mathématique de France 22:3–143.
  • Cohen, M., Montgomery, S. (1984). Group-graded rings, smash products, and group actions. Trans. Am. Math. Soc. 282:237–258.
  • Connell, I. G. (1963). On the group ring. Canad. J. Math. 15:650–685.
  • Diesl, A. J. (2013). Nil clean rings. J. Algebra 383:197–211.
  • Halberstadt, E. (1970). Le radical d’un anneide régulier. C. R. Acad. Sci., Paris, Sér. A, Paris 270:361–363.
  • Halberstadt, E. (1971). Théorie artinienne homogène des anneaux gradués à grades non commutatifs réguliers. Ph.D. Thesis. University of Pierre and Marie Currie (Paris VI).
  • Han, J., Nicholson, W. K. (2001). Extensions of clean rings. Commun. Algebra 29(6):2589–2595.
  • Ilić-Georgijević, E. (2015). A note on the Jacobson radical of a graded ring. Sarajevo J. Math. 11(2):165–170.
  • Ilić-Georgijević, E. (2016). On graded Brown–McCoy radicals of graded rings. J. Algebra Appl. 15(8): 16501437, 13.
  • Ilić-Georgijević, E. (2017). On graded Thierrin radicals of graded rings. Commun. Algebra 45(9):3886–3891.
  • Ilić-Georgijević, E. (2017). On graded special radicals of graded rings. J. Algebra Appl. doi: 10.1142/S021949881850109..
  • Kelarev, A. V. (1994). Combinatorial properties and homomorphisms of semigroups. Int. J. Algebra Comput. 4(3):443–450.
  • Kelarev, A. V. (1995). On groupoid graded rings. J. Algebra 178:391–399.
  • Kelarev, A. V. (2002). Ring Constructions and Applications, Series in Algebra, Vol. 9. New Jersey, London, Singapore, Hong Kong: World Scientific.
  • Kelarev, A. V., Okninski, J. (1995). On group graded rings satisfying polynomial identities. Glasgow Math. J. 37:205–210.
  • Kelarev, A. V., Plant, A. (1995). Bergman’s lemma for graded rings. Commun. Algebra 23(12):4613–4624.
  • Koşan, M. T., Lee, T.-K., Zhou, Y. (2014). When is every matrix over a division ring a sum of an idempotent and a nilpotent? Linear Algebra Appl. 450:7–12.
  • Koşan, M. T., Wang, Z., Zhou, Y. (2016). Nil-clean and strongly nil-clean rings. J. Pure Appl. Algebra 220(2):633–646.
  • Krasner, M. (1944). Une généralisation de la notion de corps-corpoíde. Un corpoíde remarquable de la théorie des corps valués. C. R. Acad. Sci. 219:345–347.
  • Krasner, M. (1980). Anneaux gradués généraux, Publications mathématiques et informatiques de Rennes. Colloque d’algèbre, Fascicule S3, pp. 209–308.
  • Krasner, M., Vuković, M. (1987). Structures paragraduées (groupes, anneaux, modules), Queen’s Papers in Pure and Applied Mathematics, Vol. 77. Kingston, Ontario, Canada: Queen’s University.
  • Lam, T. Y. (1991). A First Course in Noncommutative Rings, Graduate Texts in Mathematics, Vol. 131. New York: Springer-Verlag.
  • Matczuk, J. (2017). Conjugate (nil) clean rings and Köthe’s problem. J. Algebra Appl. 16(2): 1750073, 14.
  • McGovern, W. Wm., Raja, S., Sharp, A. (2015). Commutative nil clean group rings. J. Algebra Appl. 14(6): 1550094, 5.
  • Năstăsescu, C. (1984). Group rings of graded rings. Applications. J. Pure Appl. Algebra 33:313–335.
  • Năstăsescu, C., Van Oystaeyen, F. (2004). Methods of Graded Rings, Lecture Notes in Mathematics, Vol. 1836. Berlin, Heidelberg: Springer.
  • Nicholson, W. K. (1977). Lifting idempotents and exchange rings. Trans. Am. Math. Soc. 229:269–278.
  • Şahinkaya, S., Tang, G., Zhou, Y. (2017). Nil-clean group rings. J. Algebra Appl. 16(5): 1750135, 7.
  • Vuković, M. (2001). Structures graduées et paragraduées, Prepublication de l’Institut Fourier, Université de Grenoble I, Vol. 536, pp. 1–40.
  • Xiao, G., Tong, W. (2005). n-Clean rings and weakly unit stable range rings. Commun. Algebra 33(5):1501–1517.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.