Cotorsion Theories Cogenerated by a Torsionfree Class |
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| Authors: | Xianhui Fu Haiyan Zhu Mingyan Sun |
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| Institution: | 1. School of Mathematics and Statistics , Northeast Normal University , Changchun, China fuxianhui@gmail.com;3. Department of Mathematics , Zhejiang University of Technology , Hangzhou, China;4. Nanfang College , Sun Yat-sen University , Guangzhou, China |
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| Abstract: | Let R be a right perfect ring, and let (?, 𝒞) be a cotorsion theory in the category of right R-modules ? R . In this article, it is shown that every right R-module has a superfluous ?-cover if and only if there exists a torsion theory (𝒜, ?) such that (?, 𝒞) is cogenerated by ?. It is also proved that if (𝒜, ?) is a cosplitting torsion theory, then (⊥?, (⊥?)⊥) is a hereditary and complete cotorsion theory, and if (𝒜, ?) is a centrally splitting torsion theory, then (⊥?, (⊥?)⊥) is a hereditary and perfect cotorsion theory. |
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| Keywords: | Cotorsion theory Superfluous ?-cover Torsion theory |
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