In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated...In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated module over a principal ideal domain.展开更多
In this paper, the module coradical is introduced. From this, we show that any Hopf module coalgebra which is local finite can be uniquely decomposed into a direct sum of its indecomposable components. This result is ...In this paper, the module coradical is introduced. From this, we show that any Hopf module coalgebra which is local finite can be uniquely decomposed into a direct sum of its indecomposable components. This result is a generalization of the decompostion theorem of coalgebra.展开更多
Let R be a ring and n,k be two non-negative integers.As an extension of several known notions,we introduce and study(n,k)-weak cotorsion modules using the class of right R-modules with n-weak fat dimensions at most k....Let R be a ring and n,k be two non-negative integers.As an extension of several known notions,we introduce and study(n,k)-weak cotorsion modules using the class of right R-modules with n-weak fat dimensions at most k.Various examples and applications are also given.展开更多
Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C ...Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C R regular ring,and the relations between C R regular ring and C R FP injective module.展开更多
The research presented here is focused on the vibration condition of a small volume solder solder ball,which is placed on the surface of a soldering pad and is exerted a pulse modulated continuous wave laser heat sour...The research presented here is focused on the vibration condition of a small volume solder solder ball,which is placed on the surface of a soldering pad and is exerted a pulse modulated continuous wave laser heat source. Finite element method is applied to analyzed the temperature field in the solder ball, and experi- ment is conducted to test the vibration. the results show that,that, the temperature field flucturates with the same frequency as that of the laser pulse, which in turn causes a forced vibration of the same frequency in the liquid solder ball.展开更多
There are no simple singular Whittaker modules over most of important algebras,such as simple complex finite-dimensional Lie algebras,affine Kac-Moody Lie algebras,the Virasoro algebra,the Heisenberg-Virasoro algebra ...There are no simple singular Whittaker modules over most of important algebras,such as simple complex finite-dimensional Lie algebras,affine Kac-Moody Lie algebras,the Virasoro algebra,the Heisenberg-Virasoro algebra and the Schrödinger-Witt algebra.In this paper,however,we construct simple singular Whittaker modules over the Schrödinger algebra.Moreover,simple singular Whittaker modules over the Schrödinger algebra are classified.As a result,simple modules for the Schrödinger algebrawhich are locally finite over the positive part are completely classified.We also give characterizations of simple highestweight modules and simple singular Whittaker modules.展开更多
文摘In this note, we provide an effective proof of the fundamental structure theorem of finitely generated modules over a principal ideal domain, from which we find the minimality of decomposition for a finitely generated module over a principal ideal domain.
文摘In this paper, the module coradical is introduced. From this, we show that any Hopf module coalgebra which is local finite can be uniquely decomposed into a direct sum of its indecomposable components. This result is a generalization of the decompostion theorem of coalgebra.
文摘Let R be a ring and n,k be two non-negative integers.As an extension of several known notions,we introduce and study(n,k)-weak cotorsion modules using the class of right R-modules with n-weak fat dimensions at most k.Various examples and applications are also given.
文摘Using module class C R=Mx∈M,xRT=0,T∈I , we introduced the concepts of C R finitely generated module, C R finitely presented module and C R regular ring. We also discussed the criterion for C R regular ring,and the relations between C R regular ring and C R FP injective module.
文摘The research presented here is focused on the vibration condition of a small volume solder solder ball,which is placed on the surface of a soldering pad and is exerted a pulse modulated continuous wave laser heat source. Finite element method is applied to analyzed the temperature field in the solder ball, and experi- ment is conducted to test the vibration. the results show that,that, the temperature field flucturates with the same frequency as that of the laser pulse, which in turn causes a forced vibration of the same frequency in the liquid solder ball.
基金This work was supported in part the National Natural Science Foundation of China(Grant Nos.11871249,11771142)the Jiangsu Natural Science Foundation(No.BK20171294).
文摘For all generic q∈C^∗,when g is not of type A1;we prove that the quantum toroidal algebra Uq(gtor)has no nontrivial finite dimensional simple module.
文摘There are no simple singular Whittaker modules over most of important algebras,such as simple complex finite-dimensional Lie algebras,affine Kac-Moody Lie algebras,the Virasoro algebra,the Heisenberg-Virasoro algebra and the Schrödinger-Witt algebra.In this paper,however,we construct simple singular Whittaker modules over the Schrödinger algebra.Moreover,simple singular Whittaker modules over the Schrödinger algebra are classified.As a result,simple modules for the Schrödinger algebrawhich are locally finite over the positive part are completely classified.We also give characterizations of simple highestweight modules and simple singular Whittaker modules.
