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ON SI-GROUPS

Part of: Abelian groups Modules, bimodules and ideals

Published online by Cambridge University Press:  12 September 2014

R. R. ANDRUSZKIEWICZ  and
M. WORONOWICZ
R. R. ANDRUSZKIEWICZ
Affiliation:
Institute of Mathematics, University of Białystok, 15-267 Białystok, Akademicka 2,Poland email randrusz@math.uwb.edu.pl
M. WORONOWICZ*
Affiliation:
Institute of Mathematics, University of Białystok, 15-267 Białystok, Akademicka 2, Poland email mworonowicz@math.uwb.edu.pl
*
✉mworonowicz@math.uwb.edu.pl
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Abstract

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This paper presents new results concerning the structure of $\text{SI}$-groups and refines and purifies the results obtained in this field by Shalom Feigelstock [‘Additive groups of rings whose subrings are ideals’, Bull. Aust. Math. Soc.55 (1997), 477–481]. The structure theorem describing torsion-free $\text{SI}$-groups is proved in the associative case. Numerous examples of $\text{SI}$-groups are given. Some inconsistencies in Feigelstock’s article are noted and corrected.

Keywords

SI-groupsH-ringsidealstorsion-free groupsassociative ring multiplication

MSC classification

Primary: 20K99: None of the above, but in this section
Secondary: 16D25: Ideals
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 91 , Issue 1 , February 2015 , pp. 92 - 103
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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