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MATHEMATICS
Matrix representations of endomorphism rings for torsion-free abelian groups
E. A. Blagoveshchenskayaa, A. V. Mikhalevb a Emperor Alexander I St. Petersburg State Transport University, 9, Moskovskii pr., St. Petersburg, 190031, Russian Federation
b Lomonosov Moscow State University, 1, Leninskie gory, Moscow, 119991, Russian Federation
Abstract:
Non-isomorphic direct decompositions of torsion-free abelian groups are reflected in their endomorphism ring decompositions which admit matrix representations. The set of possible direct decompositions of a special kind matrix rings into direct sums of one-sided indecomposable ideals is described. This leads to the combinatorial constructions of isomorphisms between non-commutative differently decomposable ring structures.
Keywords:
torsion-free abelian groups, endomorphism rings, matrix representations.
Received: 06.12.2022 Accepted: 16.02.2023
Citation:
E. A. Blagoveshchenskaya, A. V. Mikhalev, “Matrix representations of endomorphism rings for torsion-free abelian groups”, Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 10:3 (2023), 487–498
Linking options:
https://www.mathnet.ru/eng/vspua255 https://www.mathnet.ru/eng/vspua/v10/i3/p487
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