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

  • PARK, WON-SUN (Dept. of Mathematics, Chonnam National University)
  • Received : 1999.03.31
  • Published : 1999.07.30

Abstract

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

Keywords

basic group table matrix;represented matrix

References

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