Ideal intrinsic extensions with connections to PI-rings

Journal of Pure and Applied Algebra

Volumn 213, Issue 9, 2009, Pages 1756-1776

  Armendariz, Efraim P ^a   Birkenmeier, Gary F ^b   Park, Jae Keol ^c  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b UNIVERSITY OF LOUISIANA AT LAFAYETTE   (United States)

^c Pusan National University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 64249103973     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jpaa.2009.01.010     Document Type: Article

References (39)

1. Jacobson N. Structure of Rings (1964), Amer. Math. Soc., Providence
2. Armendariz E.P., Birkenmeier G.F., and Park J.K. Rings containing ideals with bounded index. Comm. Algebra 30 (2002) 787-802
3. Rowen L.H. Some results on the center of a ring with polynomial identity. Bull. Amer. Math. Soc. 79 (1973) 219-223
4. G.F. Birkenmeier, J.K. Park, S.T. Rizvi, The structure of rings of quotients, Preprint
5. Wisbauer R. Modules and Algebras: Bimodule Structure and Group Actions on Algebras (1996), Longman, Harlow
6. Faith C., and Utumi Y. Intrinsic extensions of rings. Pacific J. Math. 14 (1964) 505-512
7. Puczylowski E.R., and Smoktunowicz A. On maximal ideals and the Brown-McCoy radical of polynomial rings. Comm. Algebra 26 (1998) 2473-2482
8. Birkenmeier G.F., Kim J.Y., and Park J.K. Quasi-Baer ring extensions and biregular rings. Bull. Austral. Math. Soc. 61 (2000) 39-52
9. Goodearl K.R. Von Neumann Regular Rings (1979), Pitman
10. DeMeyer F., and Ingraham E. Separable Algebras over Commutative Rings. Lecture Notes in Math. vol. 181 (1971), Springer-Verlag, Berlin, Heidelberg, New York
11. Armendariz E.P., and Hajarnavis C.R. A note on semiprime rings algebraic over their centres. Comm. Algebra 17 (1989) 1627-1631
12. Kaplansky I. Topological representations of algebras. II. Trans. Amer. Math. Soc. 68 (1950) 62-75
13. Martindale III W.S. On semiprime P.I. rings. Proc. Amer. Math. Soc. 40 (1973) 365-369
14. Fisher J.W. Structure of semiprime P.I. rings. Proc. Amer. Math. Soc. 39 (1973) 465-467
15. Fisher J.W. On the nilpotency of nil subrings. Canad. J. Math. 22 (1970) 1211-1216
16. Procesi C. Rings with Polynomial Identities (1973), Marcel Dekker, New York
17. Rowen L.H. Polynomial Identities in Ring Theory (1980), Academic Press, New York
18. Kaplansky I. Rings with a polynomial identity. Bull. Amer. Math. Soc. 54 (1948) 575-580
19. Schelter W., and Small L.W. Some pathological rings of quotients. J. London Math. Soc. 14 (1976) 200-202
20. Abulkheir H.E., and Birkenmeier G.F. Right complement bounded semiprime rings. Acta Math. Hungar. 70 (1996) 227-235
21. Birkenmeier G.F., Kim J.Y., and Park J.K. Principally quasi-Baer rings. Comm. Algebra 29 (2001) 639-660
22. Armendariz E.P., and Steinberg S.A. Regular self-injective rings with a polynomial identity. Trans. Amer. Math. Soc. 190 (1974) 417-425
23. Posner E.C. Prime rings satisfying a polynomial identity. Proc. Amer. Math. Soc. 11 (1960) 180-184
24. Rowen L.H. Maximal quotients of semiprime PI-algebras. Trans. Amer. Math. Soc. 196 (1974) 127-135
25. Ara P. Centers of maximal quotient rings. Arch. Math. 50 (1988) 342-347
26. Beidar K.I. Rings with generalized identities, I. Moscow Univ. Math. Bull. 32 (1977) 15-20
27. Lam T.Y. Lectures on Modules and Rings (1999), Springer-Verlag, New York
28. Stenström B. Rings of Quotients (1975), Springer-Verlag, Heidelberg, New York
29. Ferrero M., and Wisbauer R. Unitary strongly prime rings and related radicals. J. Pure Appl. Algebra 181 (2003) 209-226
30. Lam T.Y. A First Course in Noncommutative Rings (1991), Springer-Verlag, New York
31. *-Algebras. Monographs in Math. (2003), Springer-Verlag, London
32. Palmer T.W. Banach Algebras and the General Theory of *-Algebras, I (1994), Cambridge Univ. Press, Cambridge
33. Kaucikas A., and Wisbauer R. On strongly prime rings and ideals. Comm. Algebra 28 (2000) 5461-5473
34. Puczylowski E.R. Behavior of radical properties of rings under some algebraic extensions. In: Marki L., and Wiegandt R. (Eds). Radical Theory. Colloq. Math. Soc. J. Bolyai vol. 38 (1985), North-Holland, Amsterdam 449-480
35. Gardner B.J., and Wiegandt R. Radical Theory of Rings (2004), Marcel Dekker, New York
36. Drensky V., and Formanek E. Polynomial Identity Rings (2004), Birkhäuser, Basel
37. Passman D.S. The Algebraic Structures of Group Rings (1977), Wiley, New York
38. *-algebras, J. Algebra (in press)
39. Birkenmeier G.F., Müller B.J., and Rizvi S.T. Modules in which every fully invariant submodule is essential in a direct summand. Comm. Algebra 30 (2002) 1395-1415