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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We also gives a necessary condition for an LCA group to be s-pure projective in £.
📌 3 Key Takeaways
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Objective & Hypothesis:A subgroup H of a locally compact abelian (LCA) group G is called s-pure if H nG = H for every positive integer n.
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Key Findings & Data:A proper short exact sequence 0→A→φ B→C→0 in the category of LCA groups is said to be s-pure if φ(A) is an s-pure subgroup of G.
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Conclusion & Impact:We also gives a necessary condition for an LCA group to be s-pure projective in £.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:s-pure injective · s-pure projective · s-pure extension
Abstract
A subgroup H of a locally compact abelian (LCA) group G is called s-pure if H nG = H for every positive integer n. A proper short exact sequence 0→A→φ B→C→0 in the category of LCA groups is said to be s-pure if φ(A) is an s-pure subgroup of G. We establish conditions under which the s-pure exact sequences split and determine those LCA groups which are s-pure injective. We also gives a necessary condition for an LCA group to be s-pure projective in £.
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Cite This Article
ALIJANI, A., H.SAHLEH, H. (2022). s-pure extensions of locally compact abelian groups. Hacettepe Journal of Mathematics and Statistics, Cilt: 44 - Sayı: 5, 1125–1132. https://ajindex.com/articles/530236