Geodesic
A Note on Group Rings of Certain Torsion-Free Groups
Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 441-445

Voir la notice de l'article provenant de la source Cambridge University Press

As a step towards characterizing ID-groups (i.e., groups G such that, for every ring R without zero-divisors, the group ring RG has no zero-divisors), Rudin and Schneider defined Ω-groups, a possibly wider class than that of right-orderable groups, and proved that if every non-trivial finitely generated subgroup of a group G has a non-trivial H-group as an epimorphic image, then G is an ID-group. We prove that such groups are even Ω-groups and obtain the analogous result for right-orderable groups. 
Burns, R. G.; Hale, V. W. D. A Note on Group Rings of Certain Torsion-Free Groups. Canadian mathematical bulletin, Tome 15 (1972) no. 3, pp. 441-445. doi: 10.4153/CMB-1972-080-3
@article{10_4153_CMB_1972_080_3,
     author = {Burns, R. G. and Hale, V. W. D.},
     title = {A {Note} on {Group} {Rings} of {Certain} {Torsion-Free} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {441--445},
     year = {1972},
     volume = {15},
     number = {3},
     doi = {10.4153/CMB-1972-080-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-080-3/}
}
TY  - JOUR
AU  - Burns, R. G.
AU  - Hale, V. W. D.
TI  - A Note on Group Rings of Certain Torsion-Free Groups
JO  - Canadian mathematical bulletin
PY  - 1972
SP  - 441
EP  - 445
VL  - 15
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-080-3/
DO  - 10.4153/CMB-1972-080-3
ID  - 10_4153_CMB_1972_080_3
ER  - 
%0 Journal Article
%A Burns, R. G.
%A Hale, V. W. D.
%T A Note on Group Rings of Certain Torsion-Free Groups
%J Canadian mathematical bulletin
%D 1972
%P 441-445
%V 15
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-080-3/
%R 10.4153/CMB-1972-080-3
%F 10_4153_CMB_1972_080_3

[1] 1. Bernhard, Banaschewski, On proving the absence of zero-divisors for semi-group rings, Canad. Math. Bull. 4 (1961), 225-231. Google Scholar

[2] 2. Conrad, P., Right-ordered groups, Michigan Math. J. 6 (1959), 267-275. Google Scholar

[3] 3. Fuchs, L., Partially ordered algebraic systems, Pergamon Press, 1963. Google Scholar

[4] 4. Graham, Higman, The units of group rings, Proc. London Math. Soc. (2) 46 (1940), 231-248. Google Scholar

[5] 5. Karrass, A. and Solitar, D., The subgroups of a free product of two groups with an amalgamated subgroup, Trans. Amer. Math. Soc. 150(1970), 227-255. Google Scholar

[6] 6. Kurosh, A. G., The theory of groups, Vol. 2, Chelsea, New York, 1956. Google Scholar

[7] 7. LaGrange, R. H. and Rhemtulla, A. H., A remark on the group rings of order preserving permutation groups, Canad. Math. Bull. 11(1968), 679-680. Google Scholar

[8] 8. Walter, Rudin and Hans, Schneider, Idempotents in group rings, Duke Math. J. 31 (1964), 585-602. Google Scholar

Cité par Sources :