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Abelian Groups With Sufficiently π-Regular Endomorphism Ring

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Abstract

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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References

  1. Krylov, P. A., Mikhalev, A. V., and Tuganbaev, A. A. “Endomorphism Rings of Abelian Groups”, J.Math. Sci. 110, No. 3, 2683–2745 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  2. Rangaswamy, K. M. “Abelian Groups with Endomorphism Images of Special Types”, J. Algebra 6, No. 3, 271–280 (1967).

    Article  MathSciNet  MATH  Google Scholar 

  3. Fuchs, L. and Rangaswamy, K.M. “On Generalized Regular Rings”, Math. Z. 107, No. 1, 71–81 (1968).

    Article  MathSciNet  MATH  Google Scholar 

  4. Fuchs, L. Infinite Abelian Groups (Academic Press, NY, 1973; Mir, Moscow, 1977), Vol.2.

  5. Fuchs, L. Abelian Groups (Springer, New York, 2015).

    Book  MATH  Google Scholar 

  6. Glaz, S. and Wickless, W. “Regular and Principal Projective Endomorphism Rings of Mixed Abelian Groups”, Comm. in Algebra 22, No. 4, 1161–1176 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  7. V. M. Misyakov, “Abelian Groups with Regular Center of the Endomorphism Ring”, Vestn. Tomsk. gos. univ. Matem. i mekhan. 2, 33–36 (2016) [in Russian].

    Google Scholar 

  8. A. V. Karpenko and V.M. Misyakov, “On Regularity of the Center of the Endomorphism Ring of an Abelian Group”, Fundament. i prikl. matem. 13, No. 3, 39–44 (2007) [in Russian].

    MathSciNet  Google Scholar 

  9. L. Fuchs, Infinite Abelian Groups (Academic Press, NY, 1970; Mir, Moscow, 1974), Vol 1.

  10. Krylov, P. A. and Tuganbaev, A. A. “Formal Matrices and Their Determinants”, Fundament. i prikl. matem. 19, No. 1, 65–119 (2014) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Tomsk State University, pr. Lenina 36, Tomsk, 634050, Russia

    O. V. Ivanets & V. M. Misyakov

Authors
  1. O. V. Ivanets
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  2. V. M. Misyakov
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Correspondence to O. V. Ivanets.

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Original Russian Text © O.V. Ivanets, V.M. Misyakov, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2018, No. 9, pp. 21–28.

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Ivanets, O.V., Misyakov, V.M. Abelian Groups With Sufficiently π-Regular Endomorphism Ring. Russ Math. 62, 17–23 (2018). https://doi.org/10.3103/S1066369X18090037

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  • DOI: https://doi.org/10.3103/S1066369X18090037

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