52
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

ON CLASS PAIRS AND RADICALS

, &
Pages 5307-5328 | Received 01 May 2000, Published online: 01 Feb 2007

REFERENCES

  • Andrunakievich , V. A. 1966 . Radicals of Associative Rings I . Amer. Math. Soc., Transl. , 52 ( 2 ) : 95 – 128 . (Russian Original: Mat. Sb. 1958, 44, 179–212)
  • Armendariz , E. P. 1968 . Closure Properties in Radical Theory . Pacific J. Math. , 26 : 1 – 7 .
  • Birkenmeier , G. F. 1994 . Rings which are Essentially Supernilpotent . Comm. Algebra , 22 ( 3 ) : 1063 – 1082 .
  • Birkenmeier , G. F. 1994 . Radicals whose Essential Covers are Semisimple Classes . Comm. Algebra , 22 ( 15 ) : 6239 – 6258 .
  • Birkenmeier , G. F. , Heatherly , H. E. and Lee , E. K. Completely Prime Ideals and Associated Radicals . Proc. Bi-annual Ohio State-Denison Conf. 1992 . Edited by: Jain , S. K. and Rizvi , S. T. pp. 102 – 129 . New Jersey : World Scientific .
  • Birkenmeier , G. F. , Heatherly , H. E. and Lee , E. 1995 . “ Completely Prime Ideals and Radicals in Near-rings ” . In Near-Rings and Near-Fields Edited by: Fong , Y. and et al. 63 – 73 . Dordrecht : Kluwer .
  • Birkenmeier , G. F. and Wiegandt , R. 1996 . Essential Covers and Complements of Radicals . Bull. Austral. Math. Soc. , 53 : 261 – 266 .
  • de la Rosa , B. 1970 . Ideals and Radicals , Thesis Institute of Technology (Delft) .
  • Divinsky , N. J. 1965 . Rings and Radicals Toronto : University of Toronto Press .
  • Divinsky , N. and Sulinski , A. 1977 . Radical Pairs . Can. J. Math. , 29 ( 5 ) : 1086 – 1091 .
  • Dixmier , J. 1977 . Enveloping Algebras Amsterdam : North Holland .
  • Ferrero , M. and Parmenter , M. 1989 . A Note on Jacobson Rings and Polynomial Rings . Proc. Amer. Math. Soc. , 105 ( 2 ) : 281 – 286 .
  • Ferrero , M. and Puczylowski , E. R. 1998 . The Singular Ideal and Radicals . J. Austral. Math. Soc. (Series A) , 64 : 195 – 209 .
  • Gardner , B. J. and Wiegandt , R. 1982 . Characterizing and Constructing Special Radicals . Acta Math. Acad. Sci. Hungar. , 40 : 73 – 83 .
  • Goodearl , K. R. and Letzter , E. S. 1994 . Prime Factor Algebras of the Coordinate Ring of Quantum Matrices . Proc. Amer. Math. Soc. , 121 : 1017 – 1025 .
  • Handelman , D. E. and Lawrence , J. 1975 . Strongly Prime Rings . Trans. Amer. Math. Soc. , 211 : 209 – 233 .
  • Heyman , G. A.P. and Roos , C. 1977 . Essential Extensions in Radical Theory for Rings . J. Austral. Math. Soc. , 23 : 340 – 347 .
  • Jaegermann , M. and Sands , A. D. 1978 . On Normal Radicals, N-Radicals and A-Radicals . J. Algebra , 50 : 337 – 349 .
  • le Roux , H. J. , Heyman , G. A.P. and Jenkins , T. L. 1981 . Essentially Closed Classes of Rings and Upper Radicals . Acta Math. Acad. Sci. Hungar. , 38 : 63 – 68 .
  • Lorenz , M. 1981 . Completely Prime Ideals on Ore Extensions . Comm. Algebra , 11 : 1227 – 1232 .
  • Majumdar , S. and Paul , A. C. 1990 . Radicals Similar to a Radical Pair . Bull. Cal. Math. Soc. , 82 : 79 – 92 .
  • Mlitz , R. and Veldsman , S. 1990 . Radicals and Subdirect Decompositions of Ω-groups . J. Austral. Math. Soc. (Series A) , 48 : 171 – 198 .
  • Osborn , J. 1972 . Varieties of Algebras . Advances in Math. , 8 : 163 – 369 .
  • Puczylowski , E. R. 1992 . On Left Hereditariness of Pseudo-complements of Hereditary Radicals . Studia. Sci. Math. Hungar. , 27 : 201 – 205 .
  • Rjabuhin , Ju. M. and Wiegandt , R. 1981 . On Special Radicals, Supernilpotent Radicals and Weakly Homomorphically Closed Classes . J. Austral. Math. Soc. (Series A) , 31 : 152 – 162 .
  • Rowen , L. H. 1988 . Ring Theory I San Diego : Academic Press .
  • Schroder , M. 1990 . On N. I. Dubrovin's Approach to the Construction of Not-completely-prime Prime Ideals in Chain Rings . Resultate der Mathimatik , 17 : 296 – 306 .
  • Sigurdsson , G. 1984 . Differential Operator Rings whose Prime Factors have Bounded Goldie Dimension . Arch. Math. , 42 : 348 – 353 .
  • Snider , R. I. 1972 . Lattices of Radicals . Pacific J. Math. , 40 : 207 – 220 .
  • Stewart , P. N. 1970 . Semisimple Radical Classes . Pacific J. Math. , 32 : 249 – 254 .
  • Storrer , H. H. 1968 . Epimorphismen Von Kommutativen Ringen . Comment Math. Helv. , 43 : 378 – 401 .
  • van Leeuwen , L. C.A. and Wiegandt , R. 1978 . Construction and Composition of Radical and Semisimple Classes . Ann. Univ. Sci. Bud. , 21 : 65 – 75 .
  • Watters , J. F. 1975 . Polynomial Extension of Jacobson Rings . J. Algebra , 36 : 302 – 308 .
  • Watters , J. F. 1976 . The Brown-McCoy Radical and Jacobson Rings . Bull. Acad. Polon. Sci. , 23 : 94 – 100 .
  • Wiegandt , R. 1974 . “ Radical and Semisimple Classes of Rings ” . In Queen's Papers in Pure and Applied Mathematics , No. 37 Kingston : Queen's University .
  • Wiegandt , R. 1983 . Radical Theory of Rings . Math. Student , 51 : 145 – 185 .
  • Yood , B. 1999 . On Prime and Primitive Ideals . Houston J. Math. , 25 : 235 – 246 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.