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Finitely presented systems of modules and Lazard’s lemma. (English) Zbl 1424.16049

Summary: According to the fundamental lemma of Lazard, any module can be expressed as the limit of a direct system of finitely presented modules. In this paper, we propose a generalization of the \((C, D)\)-subquotient systems in Lazard’s lemma and set up a framework to study the universal property of the Lazard lemma. We prove this property for some direct systems and pose questions for the general case.

MSC:

16S15 Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
16S10 Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.)
16D10 General module theory in associative algebras
18A30 Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
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