References
Artin, E., C. Nesbitt, andR. Thrall: Rings with minimum condition. Ann Arbor: University of Michigan Press 1944.
Baer, R.: Radical ideals. Am. J. Math.65, 537–568 (1943).
Beidleman, J. C.: A radical for near-ring modules. Michigan Math. J.12, 377–383 (1965).
—— Quasi-regularity in near-rings. Math. Z.89, 224–229 (1965).
—— Distributively generated near-rings with descending chain condition. Math. Z.91, 65–69 (1966).
—— Nonsemi-simple distributively generated near-rings with minimum condition. Math. Ann.170, 206–213 (1967).
—— On the theory of radicals of distributively generated near-rings (I. The Primitive-Radical). Math. Ann.173, 89 (1967).
Blackett, D. W.: Simple and semi-simple near-rings. Proc. Am. Math. Soc.4, 772–785 (1953).
Brauer, R.: On the nilpotency of the radical of a ring. Bull. Am. Math. Soc.48, 752–758 (1942).
Fröhlich, A.: Distributively generated near-rings (I. Ideal Theory). Proc. London Math. Soc.8, 76–94 (1958).
—— Distributively generated near-rings (II. Representation Theory). Proc. London Math. Soc.8, 95–108 (1958).
Jacobson, N.: Lectures in abstract algebra (Basic Concepts). Vol. I. New York: Van Nostrand 1951.
Köthe, G.: Die Struktur der Ringe, deren Restklassenring nach dem Radikal vollständig reduzibel ist. Math. Z.32, 161–186 (1930).
Kurosh, A. G.: Theory of groups, Vol. II. New York: Chelsea 1956.
Laxton, R. R.: A radical and its theory for distributively generated near-rings. J. London Math. Soc.38, 40–49 (1963).
—— Prime ideals and the ideal-radical of a distributively generated near-ring. Math. Z.83, 8–17 (1964).
Scott, W. R.: Group theory. New Jersey: Prentice-Hall 1964.
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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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DOI: https://doi.org/10.1007/BF01361711