호남수학학술지 (Honam Mathematical Journal)

  • 제21권1호
  • /
  • Pages.57-64
  • /
  • 1999
  • /
  • 1225-293X(pISSN)
  • /
  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
권호 표지

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)
  • 투고 : 1999.03.31
  • 발행 : 1999.07.30
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초록

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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참고문헌

  1. Proc. Amer. Math. Soc. v.62 On the trace of an idempotent in group ring Cliff, G.H.;Sehgal, S.K.
  2. The Algebraic Structure of Group Rings Passman, D.S.
  3. Comm. Korean Math. Soc. v.11 On the group ring of Klein's four group Park, Won-Sun
  4. Comm. Korean Math. Soc. v.12 The units and idempotents in the group ring of a finite cyclic group Park, Won-Sun
  5. Korean Ann. Math. v.15 Idempotents in the Group Ring K$(Z_n{\times}Z_n)$ Park, Won-Sun;Im, Bok-Hee
  6. Arch Math. v.28 Group rings without nontrivial idempotent Sehgal, S.K.;Zassenhaus, H.J.
  7. Topics in Group Rings Sehgal, S.K.