130
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Radicals of Ore Extension of Skew Armendariz Rings

Pages 1302-1320 | Received 11 Jun 2013, Published online: 22 Feb 2016

REFERENCES

  • Amitsur, S. A. (1956). Algebras over infinite fields. Proc. Amer. Math. Soc. 7:35–48.
  • Anderson, D. D., Camillo, V. (1998). Armendariz rings and Gaussian rings. Comm. Algebra 26(7):2265–2272.
  • Anderson, D. D., Camillo, V. (1999). Semigroups and rings whose zero products commute. Comm. Algebra 27(6):2847–2852.
  • Armendariz, E. P. (1974). A note on extensions of Baer and p.p.-rings. J. Austral. Math. Soc. 18:470–473.
  • Bell, H. E. (1970). Near-rings in which each element is a power of itself. Bull. Austral. Math. Soc. 2:363–368.
  • Birkenmeier, G. F., Heatherly, H. E., Lee, E. K. (1993). Completely prime ideals and associated radicals. In: Jain, S. K. Rizvi, S. T. eds. Ring Theory (Granville, OH, 1992). Singapore and River Edge: World Scientific, pp. 102–129.
  • Chen, W., Tong, W. (2007). On skew Armendariz rings and rigid rings. Houston J. Math. 33(2):341–353.
  • Ghahramani, H. (2012). Skew polynomial rings of formal triangular matrix rings. J. Algebra 134:344–352.
  • Hashemi, E., Moussavi, A. (2005). Polynomial extensions of quasi-Baer rings. Acta Math. Hungar. 107(3):207–224.
  • Hong, C. Y., Kim, N. K., Kwak, T. K. (2003). On skew Armendariz rings. Comm. Algebra 31(1):103–122.
  • Hong, C. Y., Kim, N. K., Kwak, T. K. (2000). Ore extensions of Baer and p.p.-rings. J. Pure Appl. Algebra 151:215–226.
  • Hong, C. Y., Kwak, T. K., Rizvi, S. T. (2006). Extensions of generalized Armendariz rings. Algebra Colloq. 13(2):253–266.
  • Huh, C., Lee, Y., Smoktunowicz, A. (2002). Armendariz rings and semicommutative rings. Comm. Algebra 30(2):751–761.
  • Kim, N. K., Lee, Y. (2000). Armendariz rings and reduced rings. J. Algebra 223: 477–488.
  • Kim, N. K., Lee, K. H., Lee, Y. (2006). Power series rings satisfying a zero divisor property. Comm. Algebra 34:2205–2218.
  • Krempa, J. (1996). Some examples of reduced rings. Algebra Colloq. 3(4):289–300.
  • Lam, T. Y. (2000). A First Course in Noncommutative Rings. New York: Springer.
  • Lam, T. Y., Leroy, A., Matczuk, J. (1997). Primeness, semiprimeness and prime radical of ore extensions. Comm. Algebra 25(8):2459–2506.
  • Lee, T. K., Wong, T. L. (2003). On Armendariz rings. Houston J. Math. 29(3):583–593.
  • Lee, T. K., Zhou, Y. (2004). Armendariz and reduced rings. Comm. Algebra 32(6): 2287–2299.
  • Liu, Z. (2005). Armendariz rings relative to a monoid. Comm. Algebra 33(3):649–661.
  • Marks, G. (2001). On 2-Primal Ore extensions. Comm. Algebra 29(5):2113–2123.
  • Marks, G. (1999). Skew polynomial rings over 2-primal rings. Comm. Algebra 27(9):4411–4423.
  • Marks, G., Mazurek, R., Ziembowski, M. (2010). A unified approach to various generalizations of Armendariz rings. Bull. Aust. Math. Soc. 81:361–397.
  • McConnell, J. C., Robson, J. C. (1987). Noncommutative Noetherian Rings. Chichester: Wiley.
  • Nasr-Isfahani, A. R. (2013). Radicals of skew generalized power series rings. J. Algebra Appl. 12(1):1250129 (13 pages).
  • Nasr-Isfahani, A. R., Moussavi, A. (2012). A generalization of reduced rings. J. Algebra Appl. 11(4):1250070 (30 pages).
  • Nasr-Isfahani, A. R., Moussavi, A. (2011). On skew power serieswise Armendariz rings. Comm. Algebra 39(9):3114–3132.
  • Nasr-Isfahani, A. R., Moussavi, A. (2008). Ore extensions of skew Armendariz rings. Comm. Algebra 36(2):508–522.
  • Rege, M. B., Chhawchharia, S. (1997). Armendariz rings. Proc. Japan Acad. Ser. A Math. Sci. 73:14–17.
  • Smoktunowicz, A. (2000). Polynomial rings over nil rings need not be nil. J. Algebra 223:427–436.

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.