Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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THE UNITS AND IDEMPOTENTS IN THE GROUP RING K($Z_m$ $\times$ $Z_n$)

  • Park, Won-Sun (Department of Mathematics Chonnam National University)
  • Published : 2000.10.01
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Abstract

Let K be an algebraically closed filed of characteristic 0 and let G = Z(sub)m x Z(sub)n. We find the conditions under which the elements of the group ring KG are units and idempotents respectively by using the represented matrix. We can see that if $\alpha$ = ∑r(g)g $\in$ KG is an idempotent then r(1) = 0, 1/mn, 2/mn, …, (mn-1)/mn or 1.

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References

  1. Comm. in Algebra v.20 Group of units of group algebra V. Bist
  2. Proc. Amer. Math. Soc. v.62 Onthe trace of an idempotent in group ring G. H. Cliff;S. K. Sehgal
  3. Comm. In Algebra v.19 Discribing units of integral group ring of some 2-groups E. Jespers;G. Leal
  4. The Algebraic Structure of Group Ring D. S. Passman
  5. Comm. Korean Math. Soc. v.11 On the group ring of Klein's four group Won-Sun Park
  6. Comm. Korean Math. Soc. v.12 The units and idempotents in the group ring of a finite cyclic group Won-Sun Park
  7. MIHMI(Journal of Indonesian Mathematical Society) v.6 no.5 The Units and Idempotents in the Group ring of a Dihedreal group Won-Sun Park
  8. Arch. Math. v.28 Group ring without nontrivial idempotent S. K. Sehgal;H. J. Zassenhaus
  9. Topics in Group Rings S. K. Sehgal