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- W3157314095 abstract "A ring whose additive group coincides with an abelian group G is called a ring on G. An abelian group G is called a TI-group if every associative ring on G is filial. If every (associative) ring on an abelian group G is an SI-ring (a hamiltonian ring), then G is called an SI-group (an SI_H-group). In this article, TI-groups, SI_H-groups and SI-groups are described in the following classes of abelian groups: almost completely decomposable groups, separable torsionfree groups and non-measurable vector groups. Moreover, a complete description of non-reduced TI-groups, SI_H-groups and SI-groups is given. This allows us to only consider reduced groups when studying TI-groups." @default.
- W3157314095 created "2021-05-10" @default.
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- W3157314095 date "2021-01-01" @default.
- W3157314095 modified "2023-09-25" @default.
- W3157314095 title "Filial rings on direct sums and direct products of torsion-free abelian groups" @default.
- W3157314095 doi "https://doi.org/10.22405/2226-8383-2021-22-1-200-212" @default.
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