Rings Whose Every Right Ideal is a Finite Direct Sum of Automorphism-Invariant Right Ideals

Abstract

We study the rings R whose every right ideal is a finite direct sum of automorphism-invariant right R-modules. These rings are called right Σ-a-rings. We find a representation in the form of block upper triangular rings of formal matrices for the indecomposable right Artinian right hereditary right Σ-a-rings.

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Correspondence to T. H. Phan.

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Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 2, pp. 239–254.

C. Q. Truong and T. H. Phan were supported by the Vietnam National Foundation for Science and Technology Development (Grant 101.04-2017.22). A. N. Abyzov was supported by the Russian Foundation for Basic Research and the Government of the Republic of Tatarstan (Grant 18–41–160024).

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Abyzov, A.N., Phan, T.H. & Truong, C.Q. Rings Whose Every Right Ideal is a Finite Direct Sum of Automorphism-Invariant Right Ideals. Sib Math J 61, 187–198 (2020). https://doi.org/10.1134/S0037446620020019

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Keywords

  • automorphism-invariant module
  • Σ-a-ring
  • regular ring
  • hereditary Artinian ring
  • serial ring