Abstract
For a commutative ring with identity, it is consistently L∗ if and only if it is consistently O∗. This result is generalized to noncommutative rings with identity in the section 2. In the section 3, it is shown that for any abelian group G and integral domain D, the group ring D[G] is L∗ if and only if it is O∗.
Mathematics Subject Classification (2010):