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Abstract <p>We consider the class <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal{Q}\mathcal{D}1\)</EquationSource> <!--VestSPGU2570076Kompantseva-m1--> </InlineEquation> of mixed abelian quotient divisible groups of torsion-free rank 1. Groups from this class, as well as countable mixed abelian groups of rank 1 are determined by their own torsion part and the class of equivalent height-matrices, which are invariants of such groups. On the other hand, every group from <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal{Q}\mathcal{D}1\)</EquationSource> <!--VestSPGU2570076Kompantseva-m2--> </InlineEquation> can be described by its cocharacteristic. An abelian group <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(G\)</EquationSource> <!--VestSPGU2570076Kompantseva-m3--> </InlineEquation> is called a <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(TI\)</EquationSource> <!--VestSPGU2570076Kompantseva-m4--> </InlineEquation>-group if every associative ring on <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(G\)</EquationSource> <!--VestSPGU2570076Kompantseva-m5--> </InlineEquation> is filial. In the class <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathcal{Q}\mathcal{D}1\)</EquationSource> <!--VestSPGU2570076Kompantseva-m6--> </InlineEquation> <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(TI\)</EquationSource> <!--VestSPGU2570076Kompantseva-m7--> </InlineEquation>-groups are described in the language of these invariants.</p>

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TI-Groups in the Class of Quotient Divisible Abelian Groups

  • 期刊论文

  • 发表日期：

    2026年3月12日

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  • E. Kompantseva,
  • T. Q. T. Nguyen

摘要

Abstract

We consider the class \(\mathcal{Q}\mathcal{D}1\) of mixed abelian quotient divisible groups of torsion-free rank 1. Groups from this class, as well as countable mixed abelian groups of rank 1 are determined by their own torsion part and the class of equivalent height-matrices, which are invariants of such groups. On the other hand, every group from \(\mathcal{Q}\mathcal{D}1\) can be described by its cocharacteristic. An abelian group \(G\) is called a \(TI\) -group if every associative ring on \(G\) is filial. In the class \(\mathcal{Q}\mathcal{D}1\) \(TI\) -groups are described in the language of these invariants.