We introduce the concept of weak α-skew Armendariz ideals and investigate their properties. Moreover, we prove that I is a weak α-skew Armendariz ideal if and only if I[x] is a weak α-skew Armendariz ideal. As a consequence, we show that R is a weak α-skew Armendariz ring if and only if R[x] is a weak α-skew Armendariz ring.
Similar content being viewed by others
References
D. D. Anderson and V. Camillo, “Armendariz rings and Gaussian rings,” Commun. Algebra, 26, No. 7, 2265–2272 (1998).
E. P. Armendariz, “A note on extensions of Bear and P. P.-rings,” J. Austral. Math. Soc., 18, 470–473 (1974).
C. Y. Hong, N. K. Kim, and T. K. Kwak, “On skew Armendariz rings,” Commun. Algebra, 31, No. 1, 103–122 (2003).
C. Huh, H. K. Kim, and Y. Lee, “P.P.-rings and generalized P.P.-rings,” J. Pure Appl. Algebra, 167, No. 1, 37–52 (2002).
C. Huh, Y. Lee, and A. Smoktunowicz, “Armendariz rings and semicommutative rings,” J. Commun. Algebra, 30, No. 2, 751–761 (2002).
N. K. Kim and Y. Lee, “Armendariz rings and reduced rings,” J. Algebra, 223, No. 2, 477–488 (2000).
T. K. Lee and T. L. Wong, “On Armendariz rings,” Houston J. Math., 29, No. 3, 583–593 (2003).
L. Liang, L. Wang, and Z. Liu, “On a generalization of semicommutative rings,” Taiwan. J. Math., 11, No. 5, 1359–1368 (2007).
Z. Liu and R. Zhao, “On weak Armendariz rings,” Commun. Algebra, 34, No. 7, 2607–2616 (2006).
G. Mason, “Reflexive ideals,” Commun. Algebra, 9, No. 17, 1709–1724 (1981).
M. B. Rege and S. Chhawchharia, “Armendariz rings,” Proc. Jpn. Acad. Ser. A. Math. Sci., 73, No. 1, 14–17 (1997).
Author information
Authors and Affiliations
Additional information
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 3, pp. 404–414, March, 2012
Rights and permissions
About this article
Cite this article
Tavallaee, H.A., Nikmehr, M.J. & Pazoki, M. Weak α-skew Armendariz ideals. Ukr Math J 64, 456–469 (2012). https://doi.org/10.1007/s11253-012-0658-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-012-0658-5