The (Quasi-)Baerness of Skew Group Ring and Fixed Ring

ABSTRACT

In this paper, the (quasi-)Baerness of skew group ring and fixed ring is investigated. The following two results are obtained: if R is a simple ring with identity and G an outer automorphism group, then R G is a Baer ring; if R is an Artinian simple ring with identity and G an outer automorphism group, then RG is a Baer ring. Moreover, by decomposing Morita Context ring and Morita Context Theory, we provided several conditions of Morita Context ring, which is formed of skew group ring and fixed ring, to be (quasi-)Baer ring.

In this paper, the (quasi-)Baerness of skew group ring and fixed ring is investigated. The following two results are obtained: if R is a simple ring with identity and G an outer automorphism group, then R G is a Baer ring; if R is an Artinian simple ring with identity and G an outer automorphism group, then RG is a Baer ring. Moreover, by decomposing Morita Context ring and Morita Context Theory, we provided several conditions of Morita Context ring, which is formed of skew group ring and fixed ring, to be (quasi-)Baer ring.

Cite this paper

nullH. Jin and Q. Zhao, "The (Quasi-)Baerness of Skew Group Ring and Fixed Ring,"*Advances in Pure Mathematics*, Vol. 1 No. 6, 2011, pp. 363-366. doi: 10.4236/apm.2011.16065.

nullH. Jin and Q. Zhao, "The (Quasi-)Baerness of Skew Group Ring and Fixed Ring,"

References

[1] H. L. Jin, “Principally Quasi-Baer Skew Group Rings and Fixed Rings,” Sc.D. Dissertation, College of Science, Pusan National University, 2003.

[2] P. Ara and M. Mathieu, “Local Multipliers of C*–Alge- bras,” Springer, Berlin-Heidelberg, New York, 2003.

[3] K. Morita, “Duality for Modules and Its Application to the Theory of Rings with Minimum Conditions,” Science Reports of the Tokyo Kyoiku Daigoku Section A, Vol. 6, 1958, pp. 83-142.

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[5] Y. Wang and Y. L. Ren, “Morita Context ring with a Pair of Zero Homomorphism II,” Journal of Mathematical Research and Exposition, Vol. 27, No. 4, 2007, pp. 687-692.

[6] H. Ebrahim, “A Note on p.q.-Baer Modules,” New York Journal of Mathematics, Vol. 14, 2008, pp. 403-410.

[7] T. W. Hungerford, “Algebra,” Springer-Verlag, New York, 1980.

[8] S. Montgomery, “Fixed Rings of Finite Automorphism Groups of Associative Rings,” Springer-Verlag Berlin Heidelberg, 1980.

[9] T. Y. Lam, “Lectures On Modules and Rings,” Springer- Verlag, New York, 1999. doi:10.1007/978-1-4612-0525-8

[10] S. T. Rizvi and S. R. Cosmin, “Baer and Quasi Baer Modules,” Communications in Algebra, Vol. 32, No. 1, 2004, pp. 103-123. doi:10.1081/AGB-120027854

[1] H. L. Jin, “Principally Quasi-Baer Skew Group Rings and Fixed Rings,” Sc.D. Dissertation, College of Science, Pusan National University, 2003.

[2] P. Ara and M. Mathieu, “Local Multipliers of C*–Alge- bras,” Springer, Berlin-Heidelberg, New York, 2003.

[3] K. Morita, “Duality for Modules and Its Application to the Theory of Rings with Minimum Conditions,” Science Reports of the Tokyo Kyoiku Daigoku Section A, Vol. 6, 1958, pp. 83-142.

[4] Y. Wang and Y. L. Ren, “Morita Context ring with a Pair of Zero Homomorphism I,” Journal of Jilin University (Science Edition), Vol. 44, No. 3, 2006, pp. 318-324.

[5] Y. Wang and Y. L. Ren, “Morita Context ring with a Pair of Zero Homomorphism II,” Journal of Mathematical Research and Exposition, Vol. 27, No. 4, 2007, pp. 687-692.

[6] H. Ebrahim, “A Note on p.q.-Baer Modules,” New York Journal of Mathematics, Vol. 14, 2008, pp. 403-410.

[7] T. W. Hungerford, “Algebra,” Springer-Verlag, New York, 1980.

[8] S. Montgomery, “Fixed Rings of Finite Automorphism Groups of Associative Rings,” Springer-Verlag Berlin Heidelberg, 1980.

[9] T. Y. Lam, “Lectures On Modules and Rings,” Springer- Verlag, New York, 1999. doi:10.1007/978-1-4612-0525-8

[10] S. T. Rizvi and S. R. Cosmin, “Baer and Quasi Baer Modules,” Communications in Algebra, Vol. 32, No. 1, 2004, pp. 103-123. doi:10.1081/AGB-120027854