Research ArticleOpen AccessGoogle Scholar indexed
The p.q.-Baer Property of Fixed Rings under Finite Group Action
Department of Mathematics, College of Sciences, Yanbian University, Yanji, China
Department of Mathematics, College of Sciences, Yanbian University, Yanji, China
- 1 Department of Mathematics, College of Sciences, Yanbian University, Yanji, China
- 2 Department of Mathematics, College of Sciences, Yanbian University, Yanji, China
Advances in Pure Mathematics·Volume 02 (2012)·Pages 397–400·Published 9 November 2012·DOI10.4236/apm.2012.26059
Copy link · social · email
Abstract
A ring R is called right principally quasi-Baer (simply, right p.q.-Baer) if the right annihilator of every principal right ideal of R is generated by an idempotent. For a ring R , let G be a finite group of ring automorphisms of R . We denote the fixed ring of R under G by R G . In this work, we investigated the right p.q.-Baer property of fixed rings under finite group action. Assume that R is a semiprime ring with a finite group G of X-outer ring automorphisms of R . Then we show that: 1) If R is G -p.q.-Baer, then R G is p.q.-Baer; 2) If R is p.q.-Baer, then R G are p.q.-Baer.
Keywordsp.q.-Baer PropertyFixed RingGroup Action
- G. F. Birkenmeier, J. Y. Kim and J. K. Park, “Principally Quasi-Baer Rings,” Communications in Algebra, Vol. 29, No. 2, 2001, pp. 639-660. doi:10.1081/AGB-100001530
- G. F. Birkenmeier, H. E. Heatherly, J. Y. Kim and J. K. Park, “Triangular Matrix Representations,” Journal of Algebra, Vol. 230, No. 2, 2000, pp. 558-595. doi:10.1006/jabr.2000.8328
- G. F. Birkenmeier, J. Y. Kim and J. K. Park, “Quasi-Baer Ring Extensions and Biregular Rings,” Bulletin of the Australian Mathematical Society, Vol. 61, No. 1, 2000, pp. 39-52. doi:10.1017/S0004972700022000
- G. F. Birkenmeier, J. Y. Kim and J. K. Park, “A Sheaf Representation of Quasi-Baer Rings,” Journal of Pure and Applied Algebra, Vol. 146, No. 3, 2000, pp. 209-223. doi:10.1016/S0022-4049(99)00164-4
- G. F. Birkenmeier and J. K. Park, “Triangular Matrix Representations of Ring Extensions,” Journal of Algebra, Vol. 265, No. 2, 2003, pp. 457-477. doi:10.1016/S0021-8693(03)00155-8
- G. F. Birkenmeier, J. Y. Kim and J. K. Park, “Polynomial Extensions of Baer and Quasi-Baer Rings,” Journal of Pure and Applied Algebra, Vol. 159, No. 1, 2001, pp. 25-42. doi:10.1016/S0022-4049(00)00055-4
- W. E. Clark, “Twisted Matrix Units Semigroup Algebras,” Duke Mathematical Journal, Vol. 34, No. 3, 1967, pp. 417-423. doi:10.1215/S0012-7094-67-03446-1
- A. Pollingher and A. Zaks, “On Baer and Quasi-Baer Rings,” Duke Mathematical Journal, Vol. 37, No. 1, 1970, pp. 127-138. doi:10.1215/S0012-7094-70-03718-X
- G. F. Birkenmeier, “Idempotents and Completely Semiprime Ideals,” Communications in Algebra, Vol. 11, No. 6, 1983, pp. 567-580. doi:10.1080/00927878308822865
- T. Y. Lam, “Lectures on Modules and Rings,” Springer, Berlin, 1998.
- J. W. Fisher and S. Montgomery, “Semiprime Skew Group Rings,” Journal of Algebra, Vol. 52, No. 1, 1978, pp. 241-247. doi:10.1016/0021-8693(78)90272-7
- M. Cohen, “Morita Context Related to Finite Automorphism Groups of Rings,” Pacific Journal of Mathematics, Vol. 98, No. 1, 1982, pp. 37-54.
- S. Montgomery, “Outer Automorphisms of Semi-Prime Rings,” Journal London Mathematical Society, Vol. 18, No. 2, 1978, pp. 209-220. doi:10.1112/jlms/s2-18.2.209
- H. L. Jin, J. Doh and J. K. Park, “Group Actions on Quasi-Baer Rings,” Canadian Mathematical Bulletin, Vol. 52, 2009, pp. 564-582. doi:10.4153/CMB-2009-057-6