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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, Number 9, Pages 21–28
(Mi ivm9394)
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This article is cited in 1 scientific paper (total in 1 paper)
Abelian groups with enough $\pi$-regular ring of endomorphisms
O. V. Ivanets, V. M. Misyakov Tomsk State University,
36 Lenin Ave., Tomsk, 634050 Russia
Abstract:
The concept of $\pi$-regular endomorphism ring of an abelian group, which generalizes the concept of regular endomorphism ring was introduced in the works of L. Fuchs and K. Rangaswamy. They described a periodic abelian groups with $\pi$-regular endomorphism rings and found some necessary conditions for an abelian group with $\pi$-regular endomorphism rings. In the present paper we study the abelian groups with enough $\pi$-regular endomorphism ring (i. e., a subclass of abelian groups with $\pi$-regular endomorphism ring) and find the necessary and sufficient conditions for arbitrary abelian groups with enough $\pi$-regular endomorphism ring.
Keywords:
abelian group, enough $\pi$-regular endomorphism ring.
Received: 10.05.2017
Citation:
O. V. Ivanets, V. M. Misyakov, “Abelian groups with enough $\pi$-regular ring of endomorphisms”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 9, 21–28; Russian Math. (Iz. VUZ), 62:9 (2018), 17–23
Linking options:
https://www.mathnet.ru/eng/ivm9394 https://www.mathnet.ru/eng/ivm/y2018/i9/p21
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Abstract page: | 266 | Full-text PDF : | 37 | References: | 43 | First page: | 7 |
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