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 applic...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.展开更多
We consider a one point extension algebra B of a quiver algebra Aq over a field k defined by two cycles and a quantum-like relation depending on a nonzero element q in k. We determine the Hochschild cohomology ring of...We consider a one point extension algebra B of a quiver algebra Aq over a field k defined by two cycles and a quantum-like relation depending on a nonzero element q in k. We determine the Hochschild cohomology ring of B modulo nilpotence and show that if q is a root of unity, then B is a counterexample to Snashall-Solberg＇s conjecture.展开更多
This is such a article to consider an ＂into＂ isometric mapping between two unit spheres of two infinite dimensional spaces of different types. In this article, we find a useful condition （using the Krein-Milman pro...This is such a article to consider an ＂into＂ isometric mapping between two unit spheres of two infinite dimensional spaces of different types. In this article, we find a useful condition （using the Krein-Milman property） under which an into-isometric mapping from the unit sphere of e（Γ） to the unit sphere of a normed space E can be linearly isometric extended.展开更多
基金Supported by Zhejiang Provincial Natural Science Foundation of China(LY18A010032)
文摘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.
文摘We consider a one point extension algebra B of a quiver algebra Aq over a field k defined by two cycles and a quantum-like relation depending on a nonzero element q in k. We determine the Hochschild cohomology ring of B modulo nilpotence and show that if q is a root of unity, then B is a counterexample to Snashall-Solberg＇s conjecture.
基金supported by the National Natural Science Foundation of China(10871101)the Research Fund for the Doctoral Program of Higher Education (20060055010)
文摘This is such a article to consider an ＂into＂ isometric mapping between two unit spheres of two infinite dimensional spaces of different types. In this article, we find a useful condition （using the Krein-Milman property） under which an into-isometric mapping from the unit sphere of e（Γ） to the unit sphere of a normed space E can be linearly isometric extended.
