Geodesic
A note on almost regular group rings
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 8, Tome 281 (2001), pp. 128-132

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It is proved that the group ring $R=AG$ is an almost regular ring if and only if: (i) the ring $A$ is almost regular, (ii) the group $G$ is locally finite and (iii) an order of any finite subgroup $H$ of the group $G$ is a unit in $A$. 
@article{ZNSL_2001_281_a4,
     author = {G. A. Garkusha},
     title = {A note on almost regular group rings},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {128--132},
     publisher = {mathdoc},
     volume = {281},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2001_281_a4/}
}
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G. A. Garkusha. A note on almost regular group rings. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 8, Tome 281 (2001), pp. 128-132. http://geodesic.mathdoc.fr/item/ZNSL_2001_281_a4/