If there is an exactly lambda-free abelian group then there is an exactly lambda-separable one
逻辑
2016-09-06 v1 环与代数
摘要
We give a solution stated in the title to problem 3 of part 1 of the problems listed in the book of Eklof and Mekler [EM],(p.453). There, in pp. 241-242, this is discussed and proved in some cases. The existence of strongly lambda-free ones was proved earlier by the criteria in [Sh:161] in [MkSh:251]. We can apply a similar proof to a large class of other varieties in particular to the variety of (non-commutative) groups.
引用
@article{arxiv.math/9503226,
title = {If there is an exactly lambda-free abelian group then there is an exactly lambda-separable one},
author = {Saharon Shelah},
journal= {arXiv preprint arXiv:math/9503226},
year = {2016}
}