E. I. Kompantseva, Pham Thi Thu Thuy, “Absolute ideals of algebraically compact Abelian groups”, Fundam. Prikl. Mat., 2019, Volume 22, Issue 5,Pages <nobr>91

This article is cited in 3 papers

Absolute ideals of algebraically compact Abelian groups

E. I. Kompantseva^ab, Pham Thi Thu Thuy^c

^a Moscow State Pedagogical Institute, Moscow, Russia
^b Financial University under the Government of the Russian Federation, Moscow, Russia
^c Ho Chi Minh City University of Pedagogy, Ho Chi Minh City, Vietnam

Abstract: An absolute ideal of an Abelian group $G$ is a subgroup that is an ideal in every ring whose additive group coincides with $G$. We describe reduced algebraically compact Abelian groups $G$ that admit at least one ring structure $R$ such that every ideal of $R$ is an absolute ideal of $G$ (Problem 93 in L. Fuchs' book “Infinite Abelian Groups”). Reduced, algebraically compact, Abelian groups that have only fully invariant subgroups as absolute ideal are characterized.

UDC: 512.541