ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 16 Laradji, Abdallah, KFUPM, Dharan, Saudi Arabia On an equational property of modules We consider a property of infinite systems of equations related to equational (or algebraic) compactness. For example, it can be shown that over any abelian group a finitely solvable system of k equations, where k is a cardinal of uncountable cofinality, always has a solvable subsystem consisting also of k equations. Some pathological (and some not so pathological) aspects of this notion when compared with equational compactness are presented. As an application, this property is used to provide a supply of ultrapowers that fail to be equationally compact.