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Abelian groups with sufficiently π-regular endomorphism ring O. V. Ivanets, V. M. Misyako

By: Ivanets, O. VContributor(s): Misyakov, V. MMaterial type: ArticleArticleContent type: Текст Media type: электронный Subject(s): абелевы группы | π-регулярные кольца эндоморфизмовGenre/Form: статьи в журналах Online resources: Click here to access online In: Russian mathematics Vol. 62, № 9. P. 17-23Abstract: The notion of π-regular endomorphism ring of an abelian group, which generalizes the notion of regular endomorphism ring, was introduced in papers of L. Fuchs and K. Rangaswamy. They described periodic abelian groups with π-regular endomorphism ring and found necessary conditions for an abelian group to have π-regular endomorphism ring. In this paper, we study abelian groups with sufficiently π-regular endomorphism ring, which form a subclass of the class of abelian groups with π-regular endomorphism ring, and find necessary and sufficient conditions for an abelian group to have sufficiently π-regular endomorphism ring.
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The notion of π-regular endomorphism ring of an abelian group, which generalizes the notion of regular endomorphism ring, was introduced in papers of L. Fuchs and K. Rangaswamy. They described periodic abelian groups with π-regular endomorphism ring and found necessary conditions for an abelian group to have π-regular endomorphism ring. In this paper, we study abelian groups with sufficiently π-regular endomorphism ring, which form a subclass of the class of abelian groups with π-regular endomorphism ring, and find necessary and sufficient conditions for an abelian group to have sufficiently π-regular endomorphism ring.

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