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A GENERALIZATION OF THE JACOBSON RADICAL

  • Naghipour, A.R. (Faculty of Mathematics and Computer Science, Amirkabir University of Technology, and Institute for Studies in Theoretical Physics and Mathematics) ;
  • Yamini, A.H. (Faculty of Mathematics and Computer Science, Amirkabir University of Technology)
  • Published : 2004.11.01

Abstract

Let R be an associative ring with identity and J(R) be the Jacobson radical of R. In this paper we investigate the generalization of the Jacobson radical of R, J* (R) say. Also we study the rings that J*(R) = J(R).

References

  1. P. Ara, Strongly $\pi$-regular rings have stable range one, Proc. Amer. Math. Soc. 124 (1996), 3293–3298
  2. G. F. Birkenmeier, J. Y. Kim and J. K. Park, Regularity conditions and the simplicity of prime factor rings, J. Pure Appl. Algebra 115 (1997), no. 3, 213–230
  3. A. P. Donsig, A. Katavolos and A. Manoussos, The Jacobson radical for analytic crossed products, J. Funct. Anal. 187 (2001), no. 1, 129–141
  4. J. W. Fisher and R. L. Snider, Rings generated by their units, J. Algebra. 42 (1976), no. 2, 363–368
  5. N. Jacobson, The radical and semi-simplicity for arbitrary ring, Amer. J. Math. 67 (1945), 300–320
  6. T. Y. Lam, A First Course in Noncommutative Rings, Grad. Texts in Math. no. 131, Springer-Verlag, Berlin, Heildelberg, New York, 1991
  7. H. Matsumura, Commutative ring theory, Cambridge University Press, Cambridge, 1986
  8. E. M. Patterson, On the radicals of certain rings of infinite matrices, Proc. Roy. Soc. Edinburgh Sect. A 65 (1960), 263–271
  9. E. M. Patterson, On the radicals of rings of row-finite matrices, Proc. Roy. Soc. Edinburgh Sect. A 66 (1961/62), 42–46
  10. M. Prest and J. Schroer, Serial functors, Jacobson radical and representation type, J. Pure Appl. Algebra. 170 (2002), no. 2-3, 295–307
  11. R. Raphael, Rings which are generated by their units, J. Algebra. 28 (1974), 199–205
  12. B. Stenstrom, Rings of quotients, Springer-Verlag, 1975
  13. A. A. Tuganbaev, Semiregular, weakly regular, and $\pi$-regular ring, Algebra, 16. J. Math. Sci. (New York). 109 (2002), no. 3, 1509–1588
  14. L. N. Vaserstein, Stable rank of rings and dimensionality of topological spaces, Funct. Anal. Appl. 5 (1971), 102–110
  15. A. R. Villena, Automatic continuity in associative and nonassociative context, Irish Math. Soc. Bull. 46 (2001), 43–76
  16. S. Yassemi, Maximal Elements of Support, Acta Math. Univ. Comenian. 67 (1998), no. 2, 231–236