The Classification of Torsion-free TI-Groups  

作　　者：Ryszard R.Andruszkiewicz Mateusz Woronowiczt 

机构地区：[1]Faculty of Mathematics,University of Bialystok 1M,Ciolkowskiego Street,15-245 Bialystok,Poland

出　　处：《Algebra Colloquium》2022年第4期595-606,共12页代数集刊（英文版）

摘　　要：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.

关 键 词：torsion-free abelian group filial ring associative ring commutative ring additivegroupsof rings 

分 类 号：O15[理学—数学]