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On Primitive Ideals in Graded Rings

  • Agata Smoktunowicz (a1)
Abstract

Let R = be a graded nil ring. It is shown that primitive ideals in R are homogeneous. Let A = be a graded non-PI just-infinite dimensional algebra and let I be a prime ideal in A. It is shown that either I = ﹛0﹜ or I = A. Moreover, A is either primitive or Jacobson radical.

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References
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[1] Bartholdi, L., Branch rings, thinned rings, tree enveloping rings. Israel J. Math. 154(2006), 93139.
[2] Divinski, N. J., Rings and Radicals. Mathematical Expositions 14, University of Toronto Press, Toronto, ON, 1965.
[3] Faith, C., Rings and Things and a Fine Array of Twentieth Century Associative Algebra. Mathematical Surveys and Monographs 65, American Mathematical Society, Providence, RI, 2004.
[4] Farkas, D. R., and Small, L. W., Algebras which are nearly finite dimensional and their identities. Israel J. Math. 127(2002), 245251.
[5] Krause, G. and Lenagan, T. H., Growth of Algebras and Gelfand-Kirillov Dimension. Revised edition. Graduate Studies in Mathematics 22, American Mathematical Society, Providence, RI, 2000.
[6] Lam, T. Y., Exercises in classical ring theory. In: Problem Books in Mathematics, Springer-Verlag, New York, 1995, pp. 122123.
[7] Reichstein, Z., Rogalski, D., and Zhang, J. J., Projectively simple rings. Adv. Math. 203(2006), no. 2, 365407.
[8] Small, L. W., Stafford, J. T., and Warfield, R. B. Jr, Affine algebras of Gelfand-Kirillov dimension one are PI. Math. Proc. Cambridge Phil. Soc. 97(1984), no. 3, 407414.
[9] Smoktunowicz, A., On primitive ideals in polynomial rings over nil rings. Algebr. Represent. Theory 8(2005), no. 1, 6973.
[10] Smoktunowicz, A. and Puczyłowski, E. R., A polynomial ring that is Jacobson radical but not nil. Israel J. Math. 124(2001), 317325.
[11] Szász, F. A., Radicals of rings. Translated by the author, Wiley Interscience Chichester, 1981.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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