Ukrainian Mathematical Journal

, Volume 66, Issue 9, pp 1354–1368 | Cite as

Generalized Semicommutative and Skew Armendariz Ideals

  • M. J. Nikmehr

We generalize the concepts of semicommutative, skew Armendariz, Abelian, reduced, and symmetric left ideals and study the relationships between these concepts.


Left Ideal Matrix Ring Quotient Ring Ring Isomorphism Polynomial Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. Aghayev, G. Gungoroglu, A. Harmanci, and S. Halicioglu, “Abelian modules,” Acta Math. Univ. Comenianae, 2, 235–244 (2009).Google Scholar
  2. 2.
    N. Aghayev, A. Harmanci, and S. Halicioglu, “On Abelian rings,” Turk. J. Math., 34, 456–474 (2010).Google Scholar
  3. 3.
    M. Baser, A. Harmanci, and T. K. Kwak, “Generalized semicommutative rings and their extensions,” Bull. Korean Math., 45, 285–297 (2008).CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    G. F. Birkenmeier, J. K. Kim, and J. K. Park, “Polynomial extensions of Baer and quasi-Baer rings,” J. Pure Appl. Algebra, 159, 25–42 (2001).CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    E. W. Clark, “Twisted matrix units semigroup algebras,” Duke Math. J., 34, 417–424 (1967).CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    J. Cui and J. Chen, On α-skew McCoy modules,” Turk. J. Math., 36, 217–229 (2012).MATHMathSciNetGoogle Scholar
  7. 7.
    C. Y. Hong, N. K. Kim, and T. K. Kwak, “On skew Armendariz rings,” Comm. Algebra, 31, No. 1, 103–122 (2003).CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    C. Huh, Y. Lee, and A. Smoktunowicz, “Armendariz rings and semicommutative rings,” Comm. Algebra, 30, 751–761 (2002).CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    M. J. Nikmehr, “The structure of ideals over a monoid with applications,” World Appl. Sci. J., 20, No. 12, 1636–1641 (2012).Google Scholar
  10. 10.
    M. J. Nikmehr, F. Fatahi, and H. Amraei, “Nil–Armendariz rings with applications to a monoid,” World Appl. Sci. J., 13, No. 12, 2509–2514 (2011).Google Scholar
  11. 11.
    H. T. Tavallaee, M. J. Nikmehr, and M. Pazoki, “Weak α-skew Armendariz ideals,” Ukr. Math. J., 64, No. 3, 456–469 (2012).CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • M. J. Nikmehr
    • 1
  1. 1.K. N. Toosi University of TechnologyTehranIran

Personalised recommendations