ORE EXTENSIONS OF PRINCIPALLY QUASI-BAER RINGS

L’Moufadal Ben Yakoub (Morocco) and Mohamed Louzari (Morocco)

Received November 2, 2007; Revised February 22, 2008

References:

[1] S. Annin, Associated primes over skew polynomial rings, Comm. Algebra 30(5) (2002), 2511-2528. [2] L. Ben Yakoub and M. Louzari, On quasi-Baer rings of Ore extensions, East-West J. Math. 8(2) (2006), 119-127. [3] G. F. Birkenmeier, J. Y. Kim and J. K. Park, On polynomial extensions of principally quasi-Baer rings, Kyungpook Math. J. 40(2) (2000), 247-253. [4] G. F. Birkenmeier, J. Y. Kim and J. K. Park, Polynomial extensions of Baer and quasi-Baer rings, J. Pure Appl. Algebra 159 (2001), 25-42. [5] G. F. Birkenmeier, J. Y. Kim and J. K. Park, Principally quasi-Baer rings, Comm. Algebra 29(2) (2001), 639-660. [6] W. E. Clark, Twisted matrix units semigroup algebras, Duke Math. Soc. 35 (1967), 417-424. [7] J. Han, Y. Hirano and H. Kim, Some results on skew polynomial rings over a reduced ring, The International Symposium on Ring Theory, Trends in Math., G. F. Birkenmeier, J. K. Park and Y. S. Park, eds., Birkhäuser, Boston, 2001. [8] E. Hashemi and A. Moussavi, Polynomial extensions of quasi-Baer rings, Acta Math. Hungar. 107(3) (2005), 207-224. [9] E. Hashemi and A. Moussavi, On -skew Armendariz rings, J. Korean Math. Soc. 42(2) (2005), 353-363. [10] C. Y. Hong, N. K. Kim and T. K. Kwak, Ore extensions of Baer and p.p.-rings, J. Pure Appl. Algebra 151(3) (2000), 215-226. [11] C. Y. Hong, N. K. Kim and T. K. Kwak, On skew Armendariz rings, Comm. Algebra 31(1) (2003), 103-122. [12] I. Kaplansky, Rings of operators, Math. Lecture Notes Series, Benjamin, New York, 1965. [13] J. Krempa, Some examples of reduced rings, Algebra Colloq. 3(4) (1996), 289-300. [14] T. Y. Lam, A. Leroy and J. Matczuk, Primeness, semiprimeness and the prime radical of Ore extensions, Comm. Algebra 25(8) (1997), 2459-2506.

Keywords and phrases: p.q.-Baer rings, Ore extensions, -skew Armendariz rings, -compatible rings, s-rigid rings.