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New examples of indecomposable torsion-free abelian groups of finite rank and rings on them

Ryszard R. Andruszkiewicz

Faculty of Mathematics, University of Bialystok, 1M, Ciolkowskiego Street, Bialystok 15-245, Poland

E-mail Address: r.andruszkiewicz@uwb.edu.pl

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and

Mateusz Woronowicz

Faculty of Computer Science, Bialystok University of Technology, 45A, Wiejska Street, Bialystok 15-351, Poland

E-mail Address: m.woronowicz@pb.edu.pl

Corresponding author.

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https://doi.org/10.1142/S0219498823502158Cited by:2 (Source: Crossref)

Abstract

The paper deals with new specific constructions of indecomposable torsion-free abelian groups of rank two and nonzero rings on them. They illustrate purely theoretical results and complement quite rare examples obtained during the classical as well as recent research of additive groups of rings. The presented results concerning the homogeneous groups remain true for groups of any finite nonzero rank. Moreover, the paper contains a construction of a torsion-free indecomposable abelian group of an arbitrary finite rank greater than two supporting an associative, but not commutative ring, as well as a ring which is neither associative nor commutative.

Communicated by A. Leroy

Keywords:

AMSC: 20K15, 13A99

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