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^∗.

中文翻译：

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扩展环上的偏序

摘要

对于身份交换环，它是一贯大号^*当且仅当它是一贯Ø ^*。这个结果在第 2 节中推广到具有恒等式的非交换环。 在第 3 节中，表明对于任何阿贝尔群G和积分域D，群环D [ G ] 是L ^∗当且仅当它是O ^* .