• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.855-864
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• 1997

Let K be a algebraically closed field of characteristic 0 and G a cyclic group of order n. We find the units and idempotent elements of the group ring KG by using the basic group table matrix of G.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.63-70
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• 1996

Let K be a field of characteristic 0 and G a Klein's four group. We find the idempotent elements and units of the group ring KG by using the basic group table matrix of G.

• Honam Mathematical Journal
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• v.21 no.1
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• pp.57-64
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• 1999

Let K be a algebraically closed field of characteristic 0 and G be abelian group $Z_2{\times}Z_2{\times}Z_2$ or $Z_2{\times}Z_4$. We find the conditions which the elements of the group ring KG are unit and idempotent respecting using the basic table matrix of G. We can see that if ${\alpha}={\sum}r(g)g$ is an idempotent element of KG, then $r(1)=0,\;\frac{1}{{\mid}G{\mid}},\;\frac{2}{{\mid}G{\mid}},\;{\cdots},\frac{{\mid}G{\mid}-1}{{\mid}G{\mid}},\;1$.