Abstract

For any totally ordered group \(G\) and its Dedekind completion \(G^\#\), we show that if \(X\) is any \(G\)-module, then the set \(M(X, G^\#)\) of all \(G\)-module maps \(X \to G^\#\), is a totally ordered group and a \(G\)-module.

中文翻译：

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$$G$$ - 模块映射

摘要

对于任何全序群\(G\)及其 Dedekind 补全\(G^\#\)，我们证明如果\(X\)是任何\(G\) -模，则集合\(M(X , G^\#)\)所有\(G\) -模块映射\(X \to G^\#\)，是一个完全有序的组和一个\(G\) -模块。