92
Views
1
CrossRef citations to date
0
Altmetric
Articles

On skew polynomials over Ikeda-Nakayama rings

, & ORCID Icon
Pages 4038-4049 | Received 08 May 2020, Accepted 22 Mar 2021, Published online: 18 Apr 2021

References

  • Baser, M., Kwa, T. K. (2011). Quasi-Armendariz property for skew polynomial rings. Comm. Korean Math. Soc. 26(4):557–573. DOI: 10.4134/CKMS.2011.26.4.557.
  • Birkenmeier, G. F., Ghirati, M., Taherifar, A. (2015). When is a sum of annihilator ideals an annihilator ideal? Commun. Algebra 43(7):2690–2702. DOI: 10.1080/00927872.2014.882931.
  • Brown, K. A., Goodearl, K. R. (2002). Lectures on Algebraic Quantum Groups. Advanced Courses in Mathematics - CRM Barcelona, 2nd ed. Basel: Birkhäuser.
  • Camillo, V., Nicholson, W. K., Yousif, M. F. (2000). Ikeda-Nakayama rings. J. Algebra 226(2):1001–1010. DOI: 10.1006/jabr.1999.8217.
  • Cortes, W. (2005). Skew Armendariz rings and annihilator ideals of skew polynomial rings. In: de la Peña, J. A., Vallejo, E., Atakishiyev, N., eds. Algebraic Structures and Their Representations. Contemporary Mathematics, Vol. 376. Providence, RI: American Mathematical Society, pp. 249–259.
  • Goodearl, K. R., Warfield, R. B., Jr. (2004). An Introduction to Noncommutative Noetherian Rings. London Mathematical Society Student Texts 61, 2nd ed. Cambridge: Cambridge University Press.
  • Hajarnavis, C. R., Norton, N. C. (1985). On dual rings and their modules. J. Algebra 93(2):253–266. DOI: 10.1016/0021-8693(85)90159-0.
  • Han, J., Hirano, Y., Kim, H. (2000). Semiprime Ore extensions. Commun. Algebra 28(8):3795–3801. DOI: 10.1080/00927870008827058.
  • Hashemi, E. (2006). Compatible ideals and radicals of Ore extensions. New York J. Math. 12:349–356.
  • Hashemi, E. (2008). Prime ideals and strongly prime ideals of skew Laurent polynomial rings. Int. J. Math. Math. Sci. 2008:835605.
  • Hashemi, E., Hamidizadeh, M., Alhevaz, A. (2017). Some types of ring elements in Ore extensions over noncommutative rings. J. Algebra Appl. 16(11):1750201. DOI: 10.1142/S0219498817502012.
  • Hashemi, E., Moussavi, A. (2005). Polynomial extensions of quasi-Baer rings. Acta Math. Hung. 107(3):207–224. DOI: 10.1007/s10474-005-0191-1.
  • Hirano, Y. (2002). On annihilator ideals of a polynomial ring over a noncommutative ring. J. Pure Appl. Algebra 168(1):45–52. DOI: 10.1016/S0022-4049(01)00053-6.
  • Hong, C. Y., Kim, N. K., Kwak, T. K. (2003). On skew Armendariz rings. Commun. Algebra 31(1):103–122. DOI: 10.1081/AGB-120016752.
  • Hong, C. Y., Kim, N. K., Lee, Y. (2010). Skew polynomial rings over semiprime rings. J. Korean Math. Soc. 47(5):879–897. DOI: 10.4134/JKMS.2010.47.5.879.
  • Ikeda, M., Nakayama, T. (1954). On some characteristic properties of quasi-Frobenius and regular rings. Proc. Am. Math. Soc. 5(1):15–19. DOI: 10.1090/S0002-9939-1954-0060489-9.
  • Kaplansky, I. (1948). Dual rings. Ann. Math. 49(3):689–701. DOI: 10.2307/1969052.
  • Kosan, T. M. (2006). The Armendariz module and its application to the Ikeda-Nakayama module. Int. J. Math. Math. Sci. 2006:1–7.
  • Leroy, A., Matczuk, J. (2005). Goldie conditions for ore extensions over semiprime rings. Algebr. Represent. Theor. 8(5):679–688. DOI: 10.1007/s10468-005-0707-y.
  • Lee, T. K., Zhou, Y. (2004). Armendariz and reduced rings. Commun. Algebra 32(6):2287–2299. DOI: 10.1081/AGB-120037221.
  • McConnell, J. C., Robson, J. C. (2001). Noncommutative Noetherian Rings. Chichester: John Wiley & Sons (1987), revised edition by the American Mathematical Society (2001).
  • Mohammadi, R., Moussavi, A., Zahiri, M. (2017). A note on minimal prime ideals. Bull. Korean Math. Soc. 54(4):1281–1291.
  • Rege, M. B., Chhawchharia, S. (1997). Armendariz rings. Proc. Japan Acad. Ser. A Math. Sci. 73(1):14–17. DOI: 10.3792/pjaa.73.14.

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.