Geodesic
ON ANNIHILATOR IDEALS OF SKEW MONOID RINGS*
Glasgow mathematical journal, Tome 52 (2010) no. 1, pp. 161-168

Voir la notice de l'article provenant de la source Cambridge University Press

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).
DOI : 10.1017/S0017089509990255
Mots-clés : 16S35, 16S36 
ZHONGKUI, LIU; XIAOYAN, YANG. ON ANNIHILATOR IDEALS OF SKEW MONOID RINGS*. Glasgow mathematical journal, Tome 52 (2010) no. 1, pp. 161-168. doi: 10.1017/S0017089509990255
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     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089509990255/}
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[1] 1.Armendariz, E. P., A note on extensions of Baer and p.p.-rings, J. Austral. Math. Soc. 18 (1974), 470–473. Google Scholar | DOI

[2] 2.Birkenmeier, G. F., Kim, J. Y. and Park, J. K., On quasi-Baer rings, Contemp. Math. 259 (2000), 67–92. Google Scholar | DOI

[3] 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] 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. Google Scholar | DOI

[5] 5.Birkenmeier, G. F., Kim, J. Y. and Park, J. K., Principally quasi-Baer rings, Comm. Algebra 29 (2001), 639–660. Google Scholar | DOI

[6] 6.Birkenmeier, G. F. and Park, J. K., Triangular matrix representations of ring extensions, J. Algebra 265 (2003), 457–477. Google Scholar | DOI

[7] 7.Clark, W. E., Twisted matrix units semigroup algebras, Duke Math. J. 34 (1967), 417–423. Google Scholar | DOI

[8] 8.Hashemi, E., The Cohn–Jordan extension and skew monoid rings over a quasi-Baer ring, Commun. Korean Math. Soc. 21 (2006), 1–9. Google Scholar | DOI

[9] 9.Hirano, Y., On ordered monoid rings over a quasi-Baer ring, Comm. Algebra 29 (2001), 2089–2095. Google Scholar | DOI

[10] 10.Hirano, Y., On annihilator ideals of a polynomial ring over a noncommutative ring, J. Pure Appl. Algebra 168 (2002), 45–52. Google Scholar | DOI

[11] 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. Google Scholar | DOI

[12] 12.Liu, Z. K., A note on principally quasi-Baer rings, Comm. Algebra 30 (2002), 3885–3890. Google Scholar | DOI

[13] 13.Liu, Z. K., Quasi-Baer rings of generalized power series, Chinese Ann. Math. 23 (2002), 579–584. Google Scholar

[14] 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] 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] 16.Stenstrom, B., Rings of Quotients (Springer-Verlag, New York, 1975). Google Scholar | DOI

[17] 17.Tominaga, H., On s-unital rings, Math. J. Okayama Univ. 18 (1976), 117–134. Google Scholar

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