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Modules over Group Rings with Certain Finiteness Conditions

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We study modules over the group ring DG all proper submodules of which are finitely generated as D-modules.

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REFERENCES

  1. P. Hall., “Finiteness conditions for soluble groups,” Proc. London. Math. Soc., 4, 419–436 (1954).

    Google Scholar 

  2. P. Hall, “On the finiteness of some soluble groups,” Proc. London. Math. Soc., 9, 595–632 (1959).

    Google Scholar 

  3. D. S. Passman, The Algebraic Structure of Group Rings, Wiley, New York (1977).

    Google Scholar 

  4. D. R. Farkas, “Noetherian group rings; an exercise in creating folklore and induction,” in: Noetherian Rings and Their Applications, Amer. Math. Soc. Math. Surveys and Monographs, Vol. 24 (1987), pp. 89–118.

    Google Scholar 

  5. K. Gruenberg, “Ring theoretic methods and finiteness conditions in infinite soluble groups,” Lect. Notes Math., 319, 75–84 (1974).

    Google Scholar 

  6. D. S. Passman, “Group rings of polycyclic groups,” in: Group Theory: Essays for Philip Hall, Academic Press, London (1984), pp. 207–256.

    Google Scholar 

  7. J. E. Roseblade, “Five lectures on group rings,” London Math. Soc. Lect. Notes Series, 121, 93–109 (1985).

    Google Scholar 

  8. D. I. Zaitsev, “Groups with complemented normal subgroups,” in: Some Problems in Group Theory [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1975), pp. 30–74.

    Google Scholar 

  9. L. A. Kurdachenko, “Locally nilpotent groups with weak minimality and maximality conditions for normal subgroups,” Dokl. Akad. Nauk Ukr. SSR, Ser. A., No. 8, 9–12 (1985).

  10. L. A. Kurdachenko, “On some classes of groups with weak minimality and maximality conditions for normal subgroups,” Ukr. Mat. Zh., 42, No. 8, 1050–1056 (1990).

    Google Scholar 

  11. D. I. Zaitsev, L. A. Kurdachenko, and A. V. Tushev, “Modules over nilpotent groups of finite rank,” Algebra Logika, 24, No. 6, 531–666 (1985).

    Google Scholar 

  12. D. I. Zaitsev, “Infinitely irreducible normal subgroups,” in: Structure of Groups and Properties of Their Subgroups [in Russian], Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1978), pp. 17–38.

    Google Scholar 

  13. L. A. Kurdachenko and I. Ya. Subbotin, Modules over Dedekind Domain, National University of Los-Angeles, Los Angeles (1996).

    Google Scholar 

  14. J. S. Wilson, “Some properties of groups inherited by normal subgroups of finite index,” Math. Z., 114, 19–21 (1970).

    Google Scholar 

  15. B. Hartley, “A dual approach to Chernikov modules,” Math. Proc. Cambridge Philos. Soc., 82, No. 2, 215–239 (1977).

    Google Scholar 

  16. B. A. F. Wehrfritz, Infinite Linear Groups, Springer, Berlin (1973).

    Google Scholar 

  17. D. J. S. Robinson and Z. Zhang, “Groups whose proper quotients have finite derived subgroups,” J. Algebra, 118, 346–368 (1988).

    Google Scholar 

  18. G. Karpilovsky, Field Theory, Marcel Dekker, New York (1988).

    Google Scholar 

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Kurdachenko, L.A. Modules over Group Rings with Certain Finiteness Conditions. Ukrainian Mathematical Journal 54, 1126–1136 (2002). https://doi.org/10.1023/A:1022014409160

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