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- W2106317541 abstract "We consider modules over commutative rings. We are looking for sufficient conditions for a continuous well-ordered ascending chain of projective modules that are pure in their union to have a projective union. First, we deal with countable chains without restriction on the sizes of the modules; in this case no extra hypothesis is needed provided R is an integral domain or ℵ 0 -noetherian (Theorem 1.3); in the latter case, the theorem covers pure-projectvity as well. We also consider chains of longer lengths over an integral domain. We establish a condition (in terms of a slightly modified κ + -freeness) for the projectivity of the union provided that the links of the chain are ≤ κ-generated and the length of the chain is κ + for an infinite cardinal κ (Theorem 1.4). Our theorems generalize several results in the literature." @default.
- W2106317541 created "2016-06-24" @default.
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- W2106317541 date "2011-02-01" @default.
- W2106317541 modified "2023-09-28" @default.
- W2106317541 title "CHAINS OF PROJECTIVE MODULES" @default.
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- W2106317541 doi "https://doi.org/10.1142/s0219498811004483" @default.
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