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Bases for modules. (English) Zbl 1101.16002

Authors’ summary: Let \(R\) be a ring and \(A\) an \(R\)-module. We examine different notions of bases or genereting sets for \(A\). Of particular interest is the notion of an irredundant basis for \(A\), that is, a subset \(X\) of \(A\) that generates \(A\) but for which no proper subset of \(X\) generates \(A\). We investigate the existence and cardinality of irredundant bases.

MSC:

16D10 General module theory in associative algebras
16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
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