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On the theory of radicals of distributively generated near-rings

II. The nil-radical

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References

  1. Artin, E., C. Nesbitt, andR. Thrall: Rings with minimum condition. Ann Arbor: University of Michigan Press 1944.

    Google Scholar 

  2. Baer, R.: Radical ideals. Am. J. Math.65, 537–568 (1943).

    Google Scholar 

  3. Beidleman, J. C.: A radical for near-ring modules. Michigan Math. J.12, 377–383 (1965).

    Google Scholar 

  4. —— Quasi-regularity in near-rings. Math. Z.89, 224–229 (1965).

    Google Scholar 

  5. —— Distributively generated near-rings with descending chain condition. Math. Z.91, 65–69 (1966).

    Google Scholar 

  6. —— Nonsemi-simple distributively generated near-rings with minimum condition. Math. Ann.170, 206–213 (1967).

    Google Scholar 

  7. —— On the theory of radicals of distributively generated near-rings (I. The Primitive-Radical). Math. Ann.173, 89 (1967).

    Google Scholar 

  8. Blackett, D. W.: Simple and semi-simple near-rings. Proc. Am. Math. Soc.4, 772–785 (1953).

    Google Scholar 

  9. Brauer, R.: On the nilpotency of the radical of a ring. Bull. Am. Math. Soc.48, 752–758 (1942).

    Google Scholar 

  10. Fröhlich, A.: Distributively generated near-rings (I. Ideal Theory). Proc. London Math. Soc.8, 76–94 (1958).

    Google Scholar 

  11. —— Distributively generated near-rings (II. Representation Theory). Proc. London Math. Soc.8, 95–108 (1958).

    Google Scholar 

  12. Jacobson, N.: Lectures in abstract algebra (Basic Concepts). Vol. I. New York: Van Nostrand 1951.

    Google Scholar 

  13. Köthe, G.: Die Struktur der Ringe, deren Restklassenring nach dem Radikal vollständig reduzibel ist. Math. Z.32, 161–186 (1930).

    Google Scholar 

  14. Kurosh, A. G.: Theory of groups, Vol. II. New York: Chelsea 1956.

    Google Scholar 

  15. Laxton, R. R.: A radical and its theory for distributively generated near-rings. J. London Math. Soc.38, 40–49 (1963).

    Google Scholar 

  16. —— Prime ideals and the ideal-radical of a distributively generated near-ring. Math. Z.83, 8–17 (1964).

    Google Scholar 

  17. Scott, W. R.: Group theory. New Jersey: Prentice-Hall 1964.

    Google Scholar 

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Beidleman, J.C. On the theory of radicals of distributively generated near-rings. Math. Ann. 173, 200–218 (1967). https://doi.org/10.1007/BF01361711

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