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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     title = {Units of the {Group} {Ring}},
     journal = {Canadian mathematical bulletin},
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     year = {1980},
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     doi = {10.4153/CMB-1980-065-0},
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