Geodesic
Absolute ideals of algebraically compact Abelian groups
Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 5, pp. 91-114

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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. 
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     author = {E. I. Kompantseva and Pham Thi Thu Thuy},
     title = {Absolute ideals of algebraically compact {Abelian} groups},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {91--114},
     publisher = {mathdoc},
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     number = {5},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2019_22_5_a9/}
}
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E. I. Kompantseva; Pham Thi Thu Thuy. Absolute ideals of algebraically compact Abelian groups. Fundamentalʹnaâ i prikladnaâ matematika, Tome 22 (2019) no. 5, pp. 91-114. http://geodesic.mathdoc.fr/item/FPM_2019_22_5_a9/