Ideal cotorsion pairs over one point extensions
Tóm tắt
Let R[P] be the one point extension of a k-algebra R by a projective R-module P. We prove that the extension of a complete ideal cotorsion pair in R-Mod is still a complete ideal cotorsion pair in R[P]-Mod. As an application, it is obtainable that the operation (−)m [P] satisfies the so-called distributive law relating the operations of products and extensions of ideals under appropriate conditions.
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