Abstract

A ring R will be called dagger if $$a^2-b^2\in 4R\Rightarrow a-b\in 2R$$ holds in R. We will show that any 2-integrally closed domain is dagger, and that, when the characteristic is not two, a 2-root closed and dagger domain is 2-integrally closed. Examples and non-examples of dagger domains are constructed.

中文翻译：

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关于2-整体闭域的性质

摘要

环R将被称为匕首，如果$${\mathrm{一种}}^2-{乙}^2\in 4\mathrm{电阻}\Rightarrow \mathrm{一种}-乙\in 2\mathrm{电阻}$$在R 中成立。我们将证明任何 2-整数闭域都是 dagger，并且当特征不是 2 时，一个 2-root 闭和 dagger 域是 2-整数闭域。构建了匕首域的示例和非示例。