Hostname: page-component-7bb8b95d7b-w7rtg Total loading time: 0 Render date: 2024-09-12T11:21:11.775Z Has data issue: false hasContentIssue false
  • English
  • Français

ON ANNIHILATOR IDEALS OF SKEW MONOID RINGS*

Published online by Cambridge University Press:  04 December 2009

LIU ZHONGKUI  and
YANG XIAOYAN
LIU ZHONGKUI
Affiliation:
Department of Mathematics, Northwest Normal University Lanzhou 730070, Gansu, People's Republic of China e-mail: [email protected]
YANG XIAOYAN
Affiliation:
Department of Mathematics, Northwest Normal University Lanzhou 730070, Gansu, People's Republic of China e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A ring R is called a left APP-ring if the left annihilator lR(Ra) is pure as a left ideal of R for every a ∈ R; R is called (left principally) quasi-Baer if the left annihilator of every (principal) left ideal of R is generated by an idempotent. Let R be a ring and M an ordered monoid. Assume that there is a monoid homomorphism φ: M ⟶ Aut(R). We give a necessary and sufficient condition for the skew monoid ring (induced by φ) to be left APP (left principally quasi-Baer, quasi-Baer, respectively).

Keywords

16S3516S36
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 1 , January 2010 , pp. 161 - 168
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Armendariz, E. P., A note on extensions of Baer and p.p.-rings, J. Austral. Math. Soc. 18 (1974), 470–473.CrossRefGoogle Scholar
2.Birkenmeier, G. F., Kim, J. Y. and Park, J. K., On quasi-Baer rings, Contemp. Math. 259 (2000), 67–92.CrossRefGoogle Scholar
3.Birkenmeier, G. F., Kim, J. Y. and Park, J. K., On polynomial extensions of principally quasi-Baer rings, Kyungpook Mathematical J. 40 (2000), 247–254.Google Scholar
4.Birkenmeier, G. F., Kim, J. Y. and Park, J. K., Polynomial extensions of Baer and quasi-Baer rings, J. Pure Appl. Algebra 159 (2001), 25–42.CrossRefGoogle Scholar
5.Birkenmeier, G. F., Kim, J. Y. and Park, J. K., Principally quasi-Baer rings, Comm. Algebra 29 (2001), 639–660.CrossRefGoogle Scholar
6.Birkenmeier, G. F. and Park, J. K., Triangular matrix representations of ring extensions, J. Algebra 265 (2003), 457–477.CrossRefGoogle Scholar
7.Clark, W. E., Twisted matrix units semigroup algebras, Duke Math. J. 34 (1967), 417–423.CrossRefGoogle Scholar
8.Hashemi, E., The Cohn–Jordan extension and skew monoid rings over a quasi-Baer ring, Commun. Korean Math. Soc. 21 (2006), 1–9.CrossRefGoogle Scholar
9.Hirano, Y., On ordered monoid rings over a quasi-Baer ring, Comm. Algebra 29 (2001), 2089–2095.CrossRefGoogle Scholar
10.Hirano, Y., On annihilator ideals of a polynomial ring over a noncommutative ring, J. Pure Appl. Algebra 168 (2002), 45–52.CrossRefGoogle Scholar
11.Hong, C. Y., Kim, N. K. and Kwak, T. K., Ore extensions of Baer and P.P.-rings, J. Pure Appl. Algebra 151 (2000), 215–226.CrossRefGoogle Scholar
12.Liu, Z. K., A note on principally quasi-Baer rings, Comm. Algebra 30 (2002), 3885–3890.CrossRefGoogle Scholar
13.Liu, Z. K., Quasi-Baer rings of generalized power series, Chinese Ann. Math. 23 (2002), 579–584.Google Scholar
14.Liu, Z. K. and Yang, X. Y., Triangular matrix representations of skew monoid rings, Math. J. Okayama Univ. 52 (2010), 97–109.Google Scholar
15.Liu, Z. K. and Zhao, R. Y., A generalization of PP-rings and p.q.-Baer rings, Glasgow J. Math. 48 (2006), 217–229.Google Scholar
16.Stenstrom, B., Rings of Quotients (Springer-Verlag, New York, 1975).CrossRefGoogle Scholar
17.Tominaga, H., On s-unital rings, Math. J. Okayama Univ. 18 (1976), 117–134.Google Scholar