Rings on vector Abelian groups
E. I. Kompantsevaab, Pham Thi Thu Thuyc
a Moscow State Pedagogical University
b Financial University under the Government of the Russian Federation, Moscow
c Ho Chi Minh City University of Education
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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E. I. Kompantseva, Pham Thi Thu Thuy, “Rings on vector Abelian groups”, Fundam. Prikl. Mat., 22:5 (2019), 91–114
Citation in format AMSBIB
\by E.~I.~Kompantseva, Pham~Thi~Thu~Thuy
\paper Rings on vector Abelian groups
\jour Fundam. Prikl. Mat.
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