关于单位群抛射的几点看法

IF 0.5 Q3 MATHEMATICS Advances in Pure and Applied Mathematics Pub Date : 2023-09-01 DOI:10.21494/iste.op.2023.1000

Naseam A. AL-Kuleab

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引用次数: 0

摘要

．本文的主要目的是研究结合环φ: R→S的单位环同态满足下列条件之一:(a)保持单位性质:φ (R ×) = S ×和(b)逆保持单位性质:φ−1 (S ×) = R ×。我们建立了这两个条件之间的关系。解决了这种情况的几个特征。给出了具有非零公共理想的环的单位群R∧S的索引的一个应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Some remarks on surjections of unit groups

. The main purpose of this paper is to study unital ring homomorphisms of associative rings ϕ : R → S satisfying one of the following conditions: (a) the unit-preserving property: ϕ ( R × ) = S × and (b) the inverse unit-preserving property: ϕ − 1 ( S × ) = R × . We establish the relationship between these two conditions. Several characterizations of such conditions are settled. An application to the index of unit groups of rings R ⊂ S having a nonzero common ideal is given.

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