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A counterexample in Jacobson radicals


Author: Phillip Schultz
Journal: Proc. Amer. Math. Soc. 122 (1994), 961-964
MSC: Primary 16N20; Secondary 20K10
MathSciNet review: 1260180
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Abstract: A plausible conjecture states that an element of the Jacobson radical of the endomorphism ring of an abelian p-group increases the height of any non-zero element of the socle. I construct a counter-example.


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  • [C] A. L. S. Corner, The independence of Kaplansky’s notions of transitivity and full transitivity, Quart. J. Math. Oxford Ser. (2) 27 (1976), no. 105, 15–20. MR 0393280
  • [F1] László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673
  • [F2] -, Infinite abelian groups, Vol. 2, Academic Press, New York, 1973.
  • [FS] László Fuchs and P. Schultz, The Jacobson radical of the endomorphism ring of a valued vector space, Algebraic structures and applications (Nedlands, 1980) Lecture Notes in Pure and Appl. Math., vol. 74, Dekker, New York, 1982, pp. 123–132. MR 647170
  • [H] Jutta Hausen, Quasi-regular ideals of some endomorphism rings, Illinois J. Math. 21 (1977), no. 4, 845–851. MR 468743
  • [HJ] Jutta Hausen and Johnny A. Johnson, Ideals and radicals of some endomorphism rings, Pacific J. Math. 74 (1978), no. 2, 365–372. MR 0480615
  • [L] Wolfgang Liebert, The Jacobson radical of some endomorphism rings, J. Reine Angew. Math. 262/263 (1973), 166–170. Collection of articles dedicated to Helmut Hasse on his seventy-fifth birthday. MR 0325665
  • [M] Charles Megibben, Large subgroups and small homomorphisms, Michigan Math. J. 13 (1966), 153–160. MR 0195939
  • [P] R. S. Pierce, Homomorphisms of primary abelian groups, Topics in Abelian Groups (Proc. Sympos., New Mexico State Univ., 1962), Scott, Foresman and Co., Chicago, Ill., 1963, pp. 215–310. MR 0177035
  • [R] Fred Richman, Thin abelian 𝑝-groups, Pacific J. Math. 27 (1968), 599–606. MR 0238948

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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1260180-2
Article copyright: © Copyright 1994 American Mathematical Society