We generalize the concepts of semicommutative, skew Armendariz, Abelian, reduced, and symmetric left ideals and study the relationships between these concepts.
Similar content being viewed by others
References
N. Aghayev, G. Gungoroglu, A. Harmanci, and S. Halicioglu, “Abelian modules,” Acta Math. Univ. Comenianae, 2, 235–244 (2009).
N. Aghayev, A. Harmanci, and S. Halicioglu, “On Abelian rings,” Turk. J. Math., 34, 456–474 (2010).
M. Baser, A. Harmanci, and T. K. Kwak, “Generalized semicommutative rings and their extensions,” Bull. Korean Math., 45, 285–297 (2008).
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).
E. W. Clark, “Twisted matrix units semigroup algebras,” Duke Math. J., 34, 417–424 (1967).
J. Cui and J. Chen, On α-skew McCoy modules,” Turk. J. Math., 36, 217–229 (2012).
C. Y. Hong, N. K. Kim, and T. K. Kwak, “On skew Armendariz rings,” Comm. Algebra, 31, No. 1, 103–122 (2003).
C. Huh, Y. Lee, and A. Smoktunowicz, “Armendariz rings and semicommutative rings,” Comm. Algebra, 30, 751–761 (2002).
M. J. Nikmehr, “The structure of ideals over a monoid with applications,” World Appl. Sci. J., 20, No. 12, 1636–1641 (2012).
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).
H. T. Tavallaee, M. J. Nikmehr, and M. Pazoki, “Weak α-skew Armendariz ideals,” Ukr. Math. J., 64, No. 3, 456–469 (2012).
Author information
Authors and Affiliations
Additional information
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 9, pp. 1213–1222, September, 2014.
Rights and permissions
About this article
Cite this article
Nikmehr, M.J. Generalized Semicommutative and Skew Armendariz Ideals. Ukr Math J 66, 1354–1368 (2015). https://doi.org/10.1007/s11253-015-1015-2
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-015-1015-2