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Mat. Zametki, 2001, Volume 70, Issue 5, Pages 736–741 (Mi mz784)  

This article is cited in 14 scientific papers (total in 14 papers)

Periodic Abelian Groups with $UA$-Rings of Endomorphisms

O. V. Ljubimtsev

Nizhny Novgorod State Pedagogical University

Abstract: A ring $R$ is said to be a unique addition ring (a $UA$-ring) if its multiplicative semigroup $(R,\cdot)$ can uniquely be endowed with a binary operation $+$ in such a way that $(R,\cdot,+)$ becomes a ring. An Abelian group is said to be an $\operatorname{End}$-$UA$-group if the endomorphism ring of the group is a $UA$-ring. In the paper we study conditions under which an Abelian group is an $\operatorname{End}$-$UA$-group.

DOI: https://doi.org/10.4213/mzm784

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English version:
Mathematical Notes, 2001, 70:5, 667–672

Bibliographic databases:

UDC: 512.541
Received: 14.03.2000
Revised: 28.11.2000

Citation: O. V. Ljubimtsev, “Periodic Abelian Groups with $UA$-Rings of Endomorphisms”, Mat. Zametki, 70:5 (2001), 736–741; Math. Notes, 70:5 (2001), 667–672

Citation in format AMSBIB
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\pages 736--741
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. V. Ljubimtsev, D. S. Chistyakov, “Abelian Groups as $\mathrm{UA}$-Modules over the Ring $\mathbb Z$”, Math. Notes, 87:3 (2010), 380–383  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. D. S. Chistyakov, “Abelevy gruppy s UA-koltsom endomorfizmov i ikh odnorodnye otobrazheniya”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2014, no. 4(30), 49–56  mathnet
    3. O. V. Ljubimtsev, D. S. Chistyakov, “Mixed Abelian Groups with Isomorphic Endomorphism Semigroups”, Math. Notes, 97:4 (2015), 556–564  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. D. S. Chistyakov, “Separable torsion-free modules with $UA$-rings of endomorphisms”, Russian Math. (Iz. VUZ), 59:6 (2015), 43–48  mathnet  crossref
    5. O. V. Ljubimtsev, “Completely Decomposable Quotient Divisible Abelian Groups with $\mathrm{UA}$-Rings of Endomorphisms”, Math. Notes, 98:1 (2015), 130–137  mathnet  crossref  crossref  mathscinet  isi  elib
    6. O. V. Ljubimtsev, D. S. Chistyakov, “Torsion-Free Modules with $\mathrm{UA}$-Rings of Endomorphisms”, Math. Notes, 98:6 (2015), 949–956  mathnet  crossref  crossref  mathscinet  isi  elib
    7. O. V. Lyubimtsev, “Algebraically compact Abelian groups with $\mathrm{UA}$-rings of endomorphisms”, J. Math. Sci., 230:3 (2018), 433–438  mathnet  crossref  mathscinet
    8. D. S. Chistyakov, “On homogeneous mappings of finitely presented modules over the ring of polyadic numbers”, J. Math. Sci., 233:1 (2018), 152–156  mathnet  crossref
    9. O. V. Lyubimtsev, D. S. Chistyakov, “$UA$-properties of modules over commutative Noetherian rings”, Russian Math. (Iz. VUZ), 60:11 (2016), 35–44  mathnet  crossref  isi
    10. D. S. Chistyakov, “On the $\mathrm{UA}$-properties of Abelian $sp$-groups and their endomorphism rings”, J. Math. Sci., 233:5 (2018), 749–754  mathnet  crossref
    11. O. V. Ljubimtsev, “Nonreduced Abelian Groups with $\mathrm{UA}$-Rings of Endomorphisms”, Math. Notes, 101:3 (2017), 484–487  mathnet  crossref  crossref  mathscinet  isi  elib
    12. O. V. Lyubimtsev, “On determinacy of completely decomposable quotient divisible abelian groups by its endomorphism semigroups”, Russian Math. (Iz. VUZ), 61:10 (2017), 65–71  mathnet  crossref  isi
    13. D. S. Chistyakov, “Odnorodnye otobrazheniya smeshannykh modulei”, Chebyshevskii sb., 18:2 (2017), 256–266  mathnet  crossref  elib
    14. D. S. Chistyakov, “Isomorphisms of semigroups of endomorphisms of mixed Abelian groups”, Russian Math. (Iz. VUZ), 62:7 (2018), 47–52  mathnet  crossref  isi
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