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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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