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.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 22, No. 5, pp. 91–114, 2019.
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Kompantseva, E.I., Thuy, P.T.T. Absolute Ideals of Algebraically Compact Abelian Groups. J Math Sci 259, 444–462 (2021). https://doi.org/10.1007/s10958-021-05634-6
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DOI: https://doi.org/10.1007/s10958-021-05634-6