Submission date: 28 June 2022

Abstract:

In this note I take the opportunity to correct the last statement of Part I of same title and continue the study of uniform purity of epimorphisms in order to derive the main result, which states that--provided R_R ∈ <K>, equivalently, <L> (the definable subcategory generated by L) contains all absolutely pure left modules--every countably generated K-Mittag-Leffler module in <L> is a direct summand of a <L>-preenvelope of a union of an L-pure ω-chain of finitely presented modules. In conclusion I present a number of examples that starts with and grew out of the study of L-purity (of monomorphisms in ℤ-Mod) for L, the definable subcategory of divisible abelian groups. Rings that get particular attention in this are RD-rings, Warfield rings and (the newly introduced) high rings.

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Full text arXiv 2206.14308: pdf, ps.