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Vietnam Journal of Mathematics 34:3(2006)
265-273
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Simply Presented Inseparable V(RG) Without R Being
Weakly Perfect or Countable
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Peter Danchev
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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.
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2000 Mathematics Subject Classification: 16U60, 16S34,
20K10.
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Keywords: Unit groups, direct sums of countable
groups, heightly-additive rings, weakly perfect rings.
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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