A counterexample in Jacobson radicals

Author:

Schultz Phillip

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference10 articles.

1. The independence of Kaplansky’s notions of transitivity and full transitivity;Corner, A. L. S.;Quart. J. Math. Oxford Ser. (2),1976

2. Pure and Applied Mathematics, Vol. 36;Fuchs, László,1970

3. \bysame, Infinite abelian groups, Vol. 2, Academic Press, New York, 1973.

4. The Jacobson radical of the endomorphism ring of a valued vector space;Fuchs, László,1982

5. Quasi-regular ideals of some endomorphism rings;Hausen, Jutta;Illinois J. Math.,1977

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