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ORE EXTENSIONS OF WEAK ZIP RINGS*

Published online by Cambridge University Press:  01 September 2009

LUNQUN OUYANG
LUNQUN OUYANG*
Affiliation:
Department of Mathematics, Hunan Normal University, Changsha, Hunan 410006, P.R. ChinaDepartment of Mathematics, Hunan University of Science and Technology, Xiangtan, Hunan 411201, P.R. China e-mail: [email protected]
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Abstract

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In this paper we introduce the notion of weak zip rings and investigate their properties. We mainly prove that a ring R is right (left) weak zip if and only if for any n, the n-by-n upper triangular matrix ring Tn(R) is right (left) weak zip. Let α be an endomorphism and δ an α-derivation of a ring R. Then R is a right (left) weak zip ring if and only if the skew polynomial ring R[x; α, δ] is a right (left) weak zip ring when R is (α, δ)-compatible and reversible.

Keywords

Primary 16S36Secondary 16S99
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 3 , September 2009 , pp. 525 - 537
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

REFERENCES

1.Beachy, J. A. and Blair, W. D., Rings whose faithful left ideals are cofaithful, Pacific J. Math. 58 (1) (1975), 1–13.Google Scholar
2.Faith, C., Rings with zero intersection property on annihilator: zip rings, Publ. Math. 33 (1989), 329–338.Google Scholar
3.Faith, C., Annihilator ideals, associated primes and Kash–McCoy commutative rings, Comm. Algebra 19 (7) (1991), 1867–1892.Google Scholar
4.Hashemi, E. and Moussavi, Polynomial extensions of quasi-Baer rings, Acta. Math. Hungar 151 (2000), 215–226.Google Scholar
5.Hirano, Y., On the uniqueness of rings of coefficients in skew polynomial rings, Pub. Math. Debrecen 54 (1999), 489–495.CrossRefGoogle Scholar
6.Hirano, Y., On annihilator ideal of a polynomial ring over a noncommutative ring, J. Pure Appl. Algebra 168 (2002), 45–52.Google Scholar
7.Hong, C. Y., Kim, N. K. and Kwark, T. K., Ore extensions of Baer and P.P-rings, J. Pure Appl. Algebra 151 (2000), 215–226.Google Scholar
8.Hong, C. Y., Kim, N. K. and Kwak, T. K., Extensions of zip rings, J. Pure Appl. Algebra 195 (3) (2005), 231–242.CrossRefGoogle Scholar
9.Huh, C., Lee, Y. and Smoktunowicz, A., Armendariz rings and semicommutative rings, Comm. Algebra 30 (2002), 751–761.Google Scholar
10.Krempa, J., Some examples of reduced rings, Algebra. Colloq. 3 (4) (1996), 289–300.Google Scholar
11.Lam, T. Y., Leory, A. and Matczuk, J., Primeness, semiprimeness and the prime radical of Ore extensions, Comm. Algebra 25 (8) (1997), 2459–2516.CrossRefGoogle Scholar
12.Liu, Z. K. and Zhao, R., On weak Armendariz rings, Comm. Algebra 34 (2006), 2607–2616.CrossRefGoogle Scholar
13.Nielsen, P. P., Semicommutativity and McCoy condition, J. Algebra 298 (2006), 134–141.Google Scholar
14.Rage, M. B. and Chhawchharia, S., Armendariz rings, Proc. Jpn Acad. Ser. A Math. Sci. 73 (1997), 14–17.Google Scholar
15.Wagner, Cortes, Skew polynomial extensions over zip rings, Int. J. Math. Math. Sci. 10 (2008), 1–8.Google Scholar
16.Zelmanowitz, J. M., The finite intersection property on annihilator right ideals, Proc. Am. Math. Soc. 57 (2) (1976), 213–216.CrossRefGoogle Scholar