效应代数上的态射性质

In the present paper the properties of morphisms in effect algebras are discussed. The conditions for the morphisms in effect algebras to be join-preservation and meet-preservation are given. From the categorical point of view, some properties of ideals, filters and congruence relations under morphisms are obtained.     

具有核的态射广义Moore-Penrose逆

本文研究了具有核的态射广义Moore-Penrose逆.利用加边态射的可逆性,获得了态射广义Moore-Penrose逆存在的一些新的充要条件及相关表达式,推广了态射Moore-Penrose逆的相应结论.     

关于正则态射的广义Moore-Penrose逆

通过态射的正则性,讨论加法范畴中态射的广义Moore-Penrose逆.给出了正则态射的广义Moore-Penrose逆存在的几个充要条件以及广义Moore-Penrose逆的表达式.     

Coherent state map quantization in a Hermitian-like setting

For vector bundles having an involution on the base space, Hermitian-like structures are defined in terms of such an involution. We prove a universality theorem for suitable self-involutive reproducing kernels on Hermitian-like vector bundles. This result relies on pullback operations involving the tautological bundle on the Grassmann manifold of a Hilbert space and exhibits the aforementioned reproducing kernels as pullbacks of universal reproducing kernels that live on the Hermitian-like tautological bundle. To this end we use a certain type of classifying morphisms, which are geometric versions of the coherent state maps from quantum theory. As a consequence of that theorem, we obtain some differential geometric properties of these reproducing kernels in this setting.     

分块态射的广义逆

ClineRE给出了分块矩阵的Moore-Penrose逆的表达式,PetrPeska引进了分块态射的记号且导出了分块态射的Moore-Penrose逆的表达式.本文中,我们推广了Cline型分块态射的记号并得到了Cline型分块态射的Moore-Penrose逆和Drazin逆以及群逆的表达式.     

范畴中态射集星型序的若干研究

本文证得星型序的乘法性质、遗传性质及其在偏序下态射广义逆的从属性质，并将星序的Hartwig上确界定理推广到带有对合*的正性预加法范畴中．     

有关不同型代数间的联系的几个问题

讨论了有关不同型代数间的联系的几个问题，分别得到了结果，并对应作了必要的说明。     

对偶扩张代数的Frobenius态射和固定点代数

设A是由箭图Q和关系I所确定的代数,D(A)是代数A的对偶扩张代数, 对应的箭图Q*和关系I*由Q和I决定．本文证明:带关系箭图(Q*,I*)的自同构由带关系箭图(Q,I)的自同构决定;D(A)的Frobenius态射由A的Frobenius态射完全决定;代数D(A)的固定点代数同构于相应的代数A的固定点代数与A°P的固定点代数的张量积,特别地,当Q为单的箭图时,代数D(A)的固定点代数同构于代数A的固定点代数的对偶扩张代数．     

R-tors到S-tors的映上的映射的存在性

给出了Golan提出的一个公开问题的证明，指出对任意有单位元的结合环，Golan提出的问题均成立．对环R的Gabriel拓扑F,讨论了商环RF的环同构．