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Fundam. Prikl. Mat., 2019, Volume 22, Issue 5, Pages 91–114 (Mi fpm1838)  

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

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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UDC: 512.541

Citation: E. I. Kompantseva, Pham Thi Thu Thuy, “Rings on vector Abelian groups”, Fundam. Prikl. Mat., 22:5 (2019), 91–114

Citation in format AMSBIB
\Bibitem{KomThu19}
\by E.~I.~Kompantseva, Pham~Thi~Thu~Thuy
\paper Rings on vector Abelian groups
\jour Fundam. Prikl. Mat.
\yr 2019
\vol 22
\issue 5
\pages 91--114
\mathnet{http://mi.mathnet.ru/fpm1838}


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