An abelian group A is called a TI-group if every associative ring with the additive group A is filial.The filiality of a ring R means that the ring R is associative and all ideals of any ideal of R are ideals in R.In ...An abelian group A is called a TI-group if every associative ring with the additive group A is filial.The filiality of a ring R means that the ring R is associative and all ideals of any ideal of R are ideals in R.In this paper,torsion-free TI-groups are described up to the structure of associative nil groups.It is also proved that,for torsion-free abelian groups that are not associative nil,the condition TI implies the indecomposability and homogeneity.The paper contains constructions of 2^(■o)such groups of any rank from 2to 2^(■o)which are pairwise non-isomorphic.展开更多
文摘An abelian group A is called a TI-group if every associative ring with the additive group A is filial.The filiality of a ring R means that the ring R is associative and all ideals of any ideal of R are ideals in R.In this paper,torsion-free TI-groups are described up to the structure of associative nil groups.It is also proved that,for torsion-free abelian groups that are not associative nil,the condition TI implies the indecomposability and homogeneity.The paper contains constructions of 2^(■o)such groups of any rank from 2to 2^(■o)which are pairwise non-isomorphic.
