Prime graded modules



In this paper, properties of prime and strongly prime graded modules are studied. The class of strongly prime graded modules that determines a graded strongly prime radical is described.


Prime Module Prime Ring Full Subcategory Prime Radical Ring Theory 
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  1. 1.
    V. A. Andrunakievich, “Prime modules and the Baer radical,” Sib. Mat. Zh., 2, No. 6, 801–806 (1961).MATHMathSciNetGoogle Scholar
  2. 2.
    V. A. Andrunakievich and Yu. M. Ryabukhin, “Special modules and special radicals,” Dokl. Akad. Nauk SSSR, 147, No. 6, 1274–1277 (1962).MATHMathSciNetGoogle Scholar
  3. 3.
    I. N. Balaba, “Special radicals of graded rings,” Bul. Acad. Ştiinţe Repub. Mold. Mat., 44, No. 1, 26–33 (2004).MathSciNetGoogle Scholar
  4. 4.
    J. Beachy, “Generating and cogenerating structures,” Trans. Am. Math. Soc., 158, 75–92 (1971).MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    J. Beachy, “Some aspects of noncommutative localization,” in: Noncommutative Ring Theory, Int. Conf., Kent, 1975, Lect. Notes Math., Vol. 545, Springer (1976), pp. 2–31.Google Scholar
  6. 6.
    L. Bican, P. Jampor, T. Kepka, and P. Neměc, “Prime and coprime modules,” Fund. Math., 57, 33–45 (1980).Google Scholar
  7. 7.
    J. Dauns, “Prime modules,” J. Reine Angew. Math., 298, 156–181 (1978).MATHMathSciNetGoogle Scholar
  8. 8.
    E. H. Feller and E. W. Swokowski, “Prime modules,” Can. J. Math., 17, 1041–1052 (1965).MATHMathSciNetGoogle Scholar
  9. 9.
    N. Groenewald and G. Heyman, “Certain classes of ideals in group rings,” Commun. Algebra, 9, 137–148 (1981).MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    D. Handelman and J. Lawrence, “Strongly prime rings,” Trans. Am. Math. Soc., 211, 209–223 (1975).MATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    R. E. Johnson, “Representations of prime rings,” Trans. Am. Math. Soc., 74, No. 2, 351–357 (1953).MATHCrossRefGoogle Scholar
  12. 12.
    S.-X. Liu and F. van Oystaeyen, “Group graded rings, smash products and additive categories,” in: Perspectives in Ring Theory, Kluwer Academic (1988), pp. 299–310.Google Scholar
  13. 13.
    C. Nǎstǎsescu and F. van Oystaeyen, “The strongly prime radical of graded rings,” Bull. Soc. Math. Belg. Ser. B, 243–251 (1984).Google Scholar
  14. 14.
    C. Nǎstǎsescu and F. van Oystaeyen, Methods of Graded Rings, Springer, Berlin (2004).Google Scholar
  15. 15.
    R. Wisbauer, “On prime modules and rings,” Commun. Algebra, 11, 2249–2265 (1983).MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    R. Wisbauer, Foundations of Module and Ring Theory, Gordon and Breach, Paris (1991).MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.L. Tolstoy Tula State Pedagogical UniversityTulaRussia

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