Group actions on quasi-Baer rings

Canadian Mathematical Bulletin

Volumn 52, Issue 4, 2009, Pages 564-582

  Jin, Hai Lan ^a   Doh, Jaekyung ^b   Park, Jae Keol ^b  

^a YANBIAN UNIVERSITY   (China)

^b Pusan National University   (South Korea)

Author keywords

(quasi ) Baer ring; C * algebra; Fixed ring; Local multiplier algebra; Skew group ring

Indexed keywords

EID: 73949112117     PISSN: 00084395     EISSN: None     Source Type: Journal    
DOI: 10.4153/CMB-2009-057-6     Document Type: Article

References (46)

1. S. A. Amitsur, On rings of quotients. In: Symposia Mathematica VIII, Academic Press, London, 1972, pp. 149-164.
2. *-algebras. Arch. Math. 54(1990), no. 4, 358-364.
3. *- algebra. Glasgow Math. J. 32(1990), no. 3, 377-379.
4. P. Ara and M. Mathieu, A local version of the Dauns-Hofmann theorem. Math. Z. 208(1991), no. 3, 349-353.
5. *-algebras. Quart. J. Math. Oxford 44(1993), no. 174, 129-138.
6. *-Algebras. Springer-Verlag, London, 2003.
7. E. P. Armendariz, A note on extensions of Baer and P.P.-rings. J. Austral. Math. Soc. 18(1974), 470-473.
8. G. M. Bergman and I. M. Issacs, Rings with fixed-point-free group actions. Proc. London Math. Soc. 27(1973), 69-87.
9. G. F. Birkenmeier, Idempotents and completely semiprime ideals. Comm. Algebra 11(1983), no. 6, 567-580.
10. -, Decompositions of Baer-like rings. Acta Math. Hungar. 59(1992), no. 3-4, 319-326.
11. G. F. Birkenmeier, G. Cǎlugǎreanu, L. Fuchs, and H. P. Goeters, The fully invariant-extending property for abelian groups. Comm. Algebra 29(2001), no. 2, 673-685.
12. G. F. Birkenmeier, H. E. Heatherly, J. Y. Kim, and J. K. Park, Triangular matrix representations. J. Algebra 230(2000), no. 2, 558-595.
13. G. F. Birkenmeier, J. Y. Kim, and J. K. Park, Quasi-Baer ring extensions and biregular rings. Bull Austral. Math. Soc. 61(2000), no. 1, 39-52.
14. -, A sheaf representation of quasi-Baer rings. J. Pure Appl. Algebra 146(2000), no. 3, 209-223.
15. -, On quasi-Baer rings. In: Algebra and its applications, Contemp. Math. 259, American Mathematical Society, Providence, RI, 2000, pp. 67-92.
16. -, Semicentral reduced algebras. In: International symposium on ring theory, Birkhäuser, Boston, MA, 2001, pp. 67-84.
17. -, Polynomial extensions of Baer and quasi-Baer rings. J. Pure AppL Algebra 159(2001), no. 1, 25-42.
18. G. F. Birkenmeier, B. J. Müller, and S. T. Rizvi, Modules in which every fully invariant submodule is essential in a direct summand. Comm. Algebra 30(2002), no. 3, 1395-1415.
19. -, Triangular matrix representations of ring extensions. J. Algebra 265(2003), no. 2, 457-477.
20. G. F. Birkenmeier, J. K. Park, and S. T. Rizvi, Ring hulls and applications. J. Algebra 304(2006), no. 2, 633-665.
21. *- algebras. To appear in J. Algebra.
22. K. A. Brown, The singular ideals of group rings. Quart. J. Math. Oxford 28(1977), no. 109,41-60.
23. V. P. Camillo, F. J. Costa-Cano, and J. J. Simon, Relating properties of a ring and its ring of row and column finite matrices. J. Algebra 244(2001), no. 2, 435-449.
24. A. W. Chatters and C. R. Hajarnavis, Rings in which every complement right ideal is a direct summand. Quart. J. Math. Oxford 28(1977), no. 109, 61-80.
25. W. E. Clark, Twisted matrix units semigroup algebras. Duke Math. J. 34(1967), 417-423.
26. M. Cohen, A Morita context related to finite automorphism groups of rings. Pacific J. Math. 98(1982), no. 1, 37-54.
27. *-algebras by example. Fields Inst. Monograph 6, American Mathematical Society, Providence, RI, 1996.
28. *-algebra. J. Functional Analysis 23(1976), no. 1, 1-10.
29. J. W. Fisher and S. Montgomery, Semiprime skew group rings. J. Algebra 52(1978), no. 1, 241-247.
30. N. J. Groenewald, A note on extensions of Baer and P.P.-rings. PubL Inst. Math. 34(1983), 71-72.
31. J. Han, Y. Hirano, and H. Kim, Semiprime ore extensions. Comm. Algebra 28(2000), no. 8, 3795-3801.
32. M. Harada, On modules with extending properties. Osaka J. Math. 19(1982), no. 1, 203-215.
33. Y. Hirano, On ordered monoid rings over a quasi-Baer ring. Comm. Algebra 29(2001), no. 5, 2089-2095.
34. I. Kaplansky, Rings of operators. W. A. Benjamin, New York, 1968.
35. T. Y. Lam, Lectures on modules and rings. Graduate Texts in Mathematics 189, Springer-Verlag, New York, 1999.
36. J. Lawrence, A singular primitive ring. Proc. Amer. Math. Soc. 45(1974), 59-62.
37. Z. Liu, A note on principally quasi-Baer rings. Comm. Algebra 30(2002), no. 8, 3885-3890.
38. K. Louden, Maximal quotient rings of ring extensions. Pacific J. Math. 62(1976), no. 2, 489-496.
39. S. Montgomery, Outer automorphisms of semi-prime rings. J. London Math. Soc. 18(1978), no. 2, 209-220.
40. B. J. Müller, The quotient category of a Morita context. J. Algebra 28(1974), 389-407.
41. J. Osterburg and J. K. Park, Morita contexts and quotient rings of fixed rings. Houston J. Math. 10(1984), no. 1,75-80.
42. *-algebras. Invent. Math. 45(1978), no. 3, 299-305.
43. A. Pollingher and A. Zaks, On Baer and quasi-Baer rings. Duke Math. J. 37(1970), 127-138.
44. *- algebras. Math. Scand. 47(1980), no. 1, 157-176.
45. S. T. Rizvi and C. S. Roman, Baer and quasi-Baer modules. Comm. Algebra 32(2004), no. 1, 103-123.
46. Z. Yi and Y. Zhou, Baer and quasi-Baer properties of group rings. J. Austral. Math. Soc. 83(2007), no. 2, 285-296.