On definability of a periodic EndE+-group by its endomorphism group |
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Authors: | E M Kolenova |
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Institution: | (1) Nizhny Novgorod State Pedagogical University, Nizhny Novgorod, Russia |
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Abstract: | Let A be a class of Abelian groups, A ∈ A, and End(A) be the additive endomorphism group of the group A. The group A is said to be defined by its endomorphism group in the class {ie208-01} if for every group B ∈ B such that End(B) ≅ End(A) the isomorphism B ≅ A holds. The paper considers the problem of definability of a periodic Abelian group A such that End-End(A) ≅ End(A). The classes of periodical Abelian groups, of divisible Abelian groups, of reduced Abelian groups, of nonreduced Abelian
groups, and of all Abelian groups are investigated in this paper.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 2, pp. 123–131, 2007. |
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