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    STUDIA MATHEMATICA - Issue no. 2 / 2006  
         
  Article:   CRITERIA FOR UNIT GROUPS IN COMMUTATIVE GROUP RINGS.

Authors:  PETER DANCHEV.
 
       
         
  Abstract:  Suppose G is an arbitrary abelian group and F is a field ofcharF = p != 0. In the present paper criteria are found the group of allunits UF[G] in the group ring F[G] and its subgroup V F[G] of normedunits to belong to some central classes of abelian groups under minimalrestrictions on F and G. In many instances these necessary and sufficientconditions are in a final form and improve or supersede well-known anddocumented classical results in this aspect such as due to Karpilovsky(Arch. Math. Basel, 1983). The criteria obtained by us are a naturalsequel to our recent results published in Glasgow Math. J. (September,2001) and are generalizations to those stated and argued by us in Math.Balkanica (June, 2000) as well.  
         
     
         
         
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