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Vietnam Journal of Mathematics 34:3(2006) 265-273

 Simply Presented Inseparable V(RG) Without R Being Weakly Perfect or Countable

Peter Danchev

Abstract.  It is constructed a special commutative unitary ring R of characteristic 2, which is not necessarily weakly perfect (hence not perfect) or countable, and it is selected a multiplicative abelian 2-group G that is a direct sum of countable groups such that V(RG), the group of all normed 2-units in the group ring RG, is a direct sum of countable groups. So, this is the first result of the present type, which prompts that the conditions for perfection or countability on R can be, probably, removed in general.

 

2000 Mathematics Subject Classification: 16U60, 16S34, 20K10.

Keywords: Unit groups, direct sums of countable groups, heightly-additive rings, weakly perfect rings.

 

 

 

 

 

 

 

 

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