A counterexample in Jacobson radicals
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- by Phillip Schultz
- Proc. Amer. Math. Soc. 122 (1994), 961-964
- DOI: https://doi.org/10.1090/S0002-9939-1994-1260180-2
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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.References
- 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 393280, DOI 10.1093/qmath/27.1.15
- László Fuchs, Infinite abelian groups. Vol. I, Pure and Applied Mathematics, Vol. 36, Academic Press, New York-London, 1970. MR 0255673 —, Infinite abelian groups, Vol. 2, Academic Press, New York, 1973.
- 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
- Jutta Hausen, Quasi-regular ideals of some endomorphism rings, Illinois J. Math. 21 (1977), no. 4, 845–851. MR 468743
- Jutta Hausen and Johnny A. Johnson, Ideals and radicals of some endomorphism rings, Pacific J. Math. 74 (1978), no. 2, 365–372. MR 480615, DOI 10.2140/pjm.1978.74.365
- Wolfgang Liebert, The Jacobson radical of some endomorphism rings, J. Reine Angew. Math. 262(263) (1973), 166–170. MR 325665, DOI 10.1515/crll.1973.262-263.166
- Charles Megibben, Large subgroups and small homomorphisms, Michigan Math. J. 13 (1966), 153–160. MR 195939
- R. S. Pierce, Homomorphisms of primary abelian groups, Topics in Abelian Groups (Proc. Sympos., New Mexico State Univ., 1962) Scott, Foresman & Co., Chicago, Ill., 1963, pp. 215–310. MR 0177035
- Fred Richman, Thin abelian $p$-groups, Pacific J. Math. 27 (1968), 599–606. MR 238948, DOI 10.2140/pjm.1968.27.599
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 122 (1994), 961-964
- MSC: Primary 16N20; Secondary 20K10
- DOI: https://doi.org/10.1090/S0002-9939-1994-1260180-2
- MathSciNet review: 1260180