Triangular matrix representations of ring extensions

Journal of Algebra

Volumn 265, Issue 2, 2003, Pages 457-477

  Birkenmeier, Gary F ^a   Park, Jae Keol ^b  

^a UNIVERSITY OF LOUISIANA AT LAFAYETTE   (United States)

^b Pusan National University   (South Korea)

Author keywords

Centralizing extension; Generalized triangular matrix representation; Normalizing extension; Piecewise domain; Piecewise prime ring; Principally quasi Baer ring; Quasi Baer ring; Quasinormalizing extension; Ring extension; Semicentral idempotent; Triangulating; Triangulating dimension; U.p. monoid ring

Indexed keywords

EID: 0038116393     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8693(03)00155-8     Document Type: Article

References (34)

1. E.P. Armendariz, A note on extensions of Baer and p.p.-rings, J. Austral. Math. Soc. 18 (1974) 470-473.
2. E.P. Armendariz, H.K. Koo, J.K. Park, Ore extensions of von Neumann regular rings, Preprint.
3. A. Behn, Polycyclic group rings whose principal ideals are projective, J. Algebra 232 (2000) 697-707.
4. S.K. Berberian, Baer *-Rings, Springer-Verlag, Berlin-Heidelberg-New York, 1972.
5. G.F. Birkenmeier, Baer rings and quasi-continuous rings have a MDSN, Pacific J. Math. 97 (1981) 283-292.
6. G.F. Birkenmeier, Idempotents and completely semiprime ideals, Comm. Algebra 11 (1983) 567-580.
7. G.F. Birkenmeier, Decompositions of Baer-like rings, Acta Math. Hungar. 59 (1992) 319-326.
8. G.F. Birkenmeier, H.E. Heatherly, J.Y. Kim, J.K. Park, Triangular matrix representations, J. Algebra 230 (2000) 558-595.
9. G.F. Birkenmeier, J.Y. Kim, J.K. Park, Quasi-Baer ring extensions and biregular rings, Bull. Austral. Math. Soc. 61 (2000) 39-52.
10. G.F. Birkenmeier, J.Y. Kim, J.K. Park, A sheaf representation of quasi-Baer rings, J. Pure Appl. Algebra 146 (2000) 209-223.
11. G.F. Birkenmeier, J.Y. Kim, J.K. Park, On quasi-Baer rings, in: D.V. Huynh, S.K. Jain, S.R. Lopez-Permouth (Eds.), Algebras and Its Applications, in: Contemp. Math., Vol. 259, Amer. Math. Soc., Providence, 2000, pp. 67-92.
12. G.F. Birkenmeier, J.Y. Kim, J.K. Park, On polynomial extensions of principally quasi-Baer rings, Kyungpook Math. J. 40 (2000) 247-253.
13. G.F. Birkenmeier, J.Y. Kim, J.K. Park, Principally quasi-Baer rings, Comm. Algebra 29 (2001) 639-660.
14. G.F. Birkenmeier, J.Y. Kim, J.K. Park, Semicentral reduced algebras, in: G.F. Birkenmeier, J.K. Park, Y.S. Park (Eds.), The International Symposium on Ring Theory, in: Trends in Math., Birkhäuser, Boston, 2001, pp. 67-84.
15. G.F. Birkenmeier, J.Y. Kim, J.K. Park, Polynomial extensions of Baer and quasi-Baer rings, J. Pure Appl. Algebra 159 (2001) 25-42.
16. G.F. Birkenmeier, J.Y. Kim, J.K. Park, Triangular matrix representations of semiprimary rings, J. Algebra and Its Appl. 1 (2002) 123-131.
17. G.F. Birkenmeier, J.Y. Kim, J.K. Park, Prime ideals of principally quasi-Baer rings, Acta Math. Hungar. 98 (2003) 217-225.
18. K.A. Brown, The singular ideals of group rings, Quart. J. Math. Oxford 28 (1977) 41-60.
19. V.P. Camillo, Semihereditary polynomial rings, Proc. Amer. Math. Soc. 45 (1974) 173-174.
20. W.E. Clark, Twisted matrix units semigroup algebras, Duke Math. J. 34 (1967) 417-424.
21. R. Gordon, L.W. Small, Piecewise domains, J. Algebra 23 (1972) 553-564.
22. N. Groenewald, A note on extensions of Bear and p.p.-rings, Publ. L'institute Math. 34 (1983) 71-72.
23. Y. Hirano, On ordered monoid rings over a quasi-Baer ring, Comm. Algebra 29 (2001) 2089-2095.
24. S. Jøndrup, p.p. rings and finitely generated flat ideals, Proc. Amer. Math. Soc. 28 (1971) 431-435.
25. I. Kaplansky, Rings of Operators, Benjamin, New York, 1965.
26. J. Krempa, D. Niewieczerzal, Rings in which annihilators are ideals and their application to semigroup rings, Bull. Acad. Polon. Sci. Math and Astronom. Phys. 25 (1977) 851-856.
27. T.Y. Lam, Lectures on Modules and Rings, Springer-Verlag, Berlin-Heidelberg-New York, 1998.
28. P.J. McCarthy, The ring of polynomials over a commutative von Neumann regular ring, Proc. Amer. Math. Soc. 39 (1973) 253-254.
29. J. Okniński, Semigroup Algebras, Marcel Dekker, New York, 1991.
30. D.S. Passman, The Algebraic Structure of Group Rings, Wiley, New York, 1977.
31. P. Pillay, On semihereditary noncommutative polynomial rings, Proc. Amer. Math. Soc. 78 (1980) 473-474.
32. A. Pollingher, A. Zaks, On Baer and quasi-Baer rings, Duke Math. J. 37 (1970) 127-138.
33. L.W. Small, Semi-hereditary rings, Bull. Amer. Math. Soc. 73 (1967) 656-658.
34. M.K. Smith, Group algebras, J. Algebra 18 (1971) 477-499.