Taiwanese Journal of Mathematics


M. Tamer Koşan and Muhittin Başer

Full-text: Open access


n this paper, we introduce the concept of a ($\alpha$-) quasi-Armendariz module, principally quasi-Baer module and syudy its some properties. In particular, we show: (1) For an $\alpha$-quasi-Armendariz module $M_R$, $M_R$ is a principally quasi-Baer module if and only if $M[x;\alpha]_{R[x;\alpha]}$ is a principally quasi-Baer module. (2) A necessary and sufficient condition for a trivial extensions to be quasi-Armendariz is obtained. Consequently, new families of quasi-Armendariz rings are presented.

Article information

Taiwanese J. Math., Volume 12, Number 3 (2008), 573-582.

First available in Project Euclid: 21 July 2017

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 16D80: Other classes of modules and ideals [See also 16G50]

(quasi)-Armendariz module (quasi)-Baer module p.p.-module


Koşan, M. Tamer; Başer, Muhittin. ON QUASI-ARMENDARIZ MODULES. Taiwanese J. Math. 12 (2008), no. 3, 573--582. doi:10.11650/twjm/1500602422. https://projecteuclid.org/euclid.twjm/1500602422

Export citation


  • D. D. Anderson and V. Camillo, Armendariz Rings and Gaussian Rings, Comm. Algebra, 26(7) (1998), 2265-2272.
  • E. P. Armendariz, A note on extensions of Baer and $p.p.$-Rings, J. Australian Math. Soc., 18 (1974), 470-473.
  • G. F. Birkenmeier, Idempotents and Completely Semiprime Ideals, Comm. Algebra, 11 (1983), 567-580.
  • G. F. Birkenmeier, J. Y. Kim and J. K. Park, Principally quasi-Baer rings, Comm. Algebra. 29(2) (2001), 639-660.
  • G. F. Birkenmeier, J. Y. Kim and J. K. Park, On Polynomial extensions of principally quasi-Baer rings, Kyungpook Math. J., 40 (2000), 247-253.
  • A. W. Chatters and C. R. Hajarnavis, Rings with Chain Conditions, Pitman, Boston, 1980.
  • W. E. Clark, Twisted matrix units semigroup algebras, Duke Math. J., 34 (1967), 417-424.
  • Y. Hirano, On annihilator ideals of a polynomial ring over a noncommutative rings, J. Pure Appl. Algebra, 168 (2002), 45-52.
  • C. Y. Hong, N. K. Kim and T. K. Kwak, Ore Extensions of Baer and $p.p.$-Rings, J. Pure Appl. Algebra, 151 (2000), 215-226.
  • S. Jøndrup, $p.p.$-Rings and finitely generated flat ideals, Proc. Amer. Math. Soc., 28 (1971), 431-435.
  • N. K. Kim and Y. Lee, Armendariz Rings and Reduced Rings, J. Algebra, 223 (2000), 477-488.
  • T. Y. Lam, Lectures on Modules and Rings, Springer-Verlag, New York, 1999.
  • T. K. Lee and Y. Zhou, Reduced Modules, Rings, modules, algebras and abelian groups, 365-377, Lecture Notes in Pure and Appl. Math., 236, Dekker, New york, (2004).
  • T. K. Lee and Y. Zhou, Armendariz and Reduced Rings, Comm. Alg., 6 (2004), 2287-2299.
  • N. H. McCoy, Remarks on divisior of zero, Amer. Math. Monthly, 49 (1942), 280-295.
  • M. B. Rege and S. Chhawchharia, Armendariz Rings, Proc. Japan Acad. Ser. A Math. Sci., 73 (1997), 14-17.
  • G. Y. Shin, Prime ideals and sheaf representation of a pseudo symetric ring, Trans. Amer. Math. Soc., 184 (1973), 43-60.