In this paper, we consider the behavior of polynomial rings over generalized quasi-Baer rings and show that the generalized quasi-Baer condition on a ring R is preserved by many polynomial extensions.
This is a preview of subscription content, log in via an institution to check access.
References
I. Kaplansky, Rings of Operators, Benjamin, New York (1965).
W. E. Clark, “Twisted matrix units semigroup algebras,” Duke Math. J., 34, 417–424 (1967).
G. F. Birkenmeier, J. Y. Kim, and J. K. Park, “Polynomial extensions of Baer and quasi-Baer rings,” J. Pure Appl. Algebra, 159, 25–42 (2001).
G. F. Birkenmeier, J. Y. Kim, and J. K. Park, “Principally quasi-Baer rings,” Commun. Algebra, 29, No. 2, 639–660 (2001).
A. Mousssavi, H. S. Javadi, and E. Hashemi, “Generalized quasi-Baer rings,” Commun. Algebra, 33, 2115–2129 (2005).
E. P. Armendariz, “A note on extensions of Baer and p.p.-rings,” J. Austral. Math. Soc., 18, 470–473 (1974).
J. Kerempa, “Some examples of reduced rings,” Algebra Colloq., 3, No. 4, 289–300 (1996).
C. Y. Hong, N. K. Kim, T. K. Kwak, “Ore extensions of Baer and p.p.-rings,” J. Pure Appl. Algebra, 151, 215–226 (2000).
Author information
Authors and Affiliations
Additional information
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 5, pp. 698–701, May, 2010.
Rights and permissions
About this article
Cite this article
Ghalandarzadeh, S., Javadi, H.S. & Khoramdel, M. Polynomial extensions of generalized quasi-Baer rings. Ukr Math J 62, 804–808 (2010). https://doi.org/10.1007/s11253-010-0390-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-010-0390-y