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Abstract
In this note we prove some universal algebraic properties of α-limits, and apply them to characterize a certain class of Σ-pure injective rings. This will provide an answer to a generalized version of a problem of Jensen and Lenzing. Our results also yield a module-theoretic characterization of singular cardinals.
ACKNOWLEDGMENT
The author gratefully acknowledges the support of King Fahd University of Petroleum and Minerals.