Geodesic
Units of the Group Ring
Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 445-448

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If R is a ring such that x, y ∈ R and xy = 0 imply yx = 0 and G≠ 1, an ordered group, then we show that ∑ αgg is a unit in RG if and only if there exists ∑ βhh in RG such that ∑ αgβg-1 = 1 and αgβh is nilpotent whenever gh≠l. We also show that if R is a ring with no nilpotent elements ≠ 0 and no idempotents ≠ 0, 1 then RG has only trivial units. Some applications are also given. 
Groenewald, N. J. Units of the Group Ring. Canadian mathematical bulletin, Tome 23 (1980) no. 4, pp. 445-448. doi: 10.4153/CMB-1980-065-0
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[1] 1. Amitsur, S. A., Radiais of polynomial rings, Canad. J. Math. 8 (1956), 355-361. Google Scholar

[2] 2. Coleman, D. B. and Enochs, E. E., Isomorphic polynomial rings, Proc. Amer. Math. Soc. 27 (1971), 247-252. Google Scholar

[3] 3. Lambek, J., Lectures on rings and modules, Blaisdell, Waltham, Mass. (1966). Google Scholar

[4] 4. Parmenter, M. M., Isomorphic group rings, Canad. Math. Bull. Vol 18(4), 1975, 567-575. Google Scholar

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