• Title, Summary, Keyword: basic group table matrix

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THE UNITS AND INEMPOTENTS IN THE GROUP RING OF A FINITE CYCLIC GROUP

  • Park, Won-Sun
    • 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.

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On the group rings of the Klein's four group

  • Park, Won-Sun
    • 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.

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THE UNITS AND IDEMPOTENTS IN THE GROUP RING OF ABELIAN GROUPS Z2×Z2×Z2 AND Z2×Z4

  • PARK, WON-SUN
    • 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 $r(1)=0,\;\frac{1}{{\mid}G{\mid}},\;\frac{2}{{\mid}G{\mid}},\;{\cdots},\frac{{\mid}G{\mid}-1}{{\mid}G{\mid}},\;1$.

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