关于核的类群集合
On the set of grouplikes of a coring
摘要：
我们把注意力集中到环$A$上的核$\coring{C}$的类群元素的集合$\gl{\coring{C}}$上。我们分别观察了$A$的单位群$U(A)$和$\aut{\coring{C}}$以及$\coring{C}$的核环的自同构群$\gl{\coring{C}}$和$\aut{\coring{C}}$在$\gl{\coring{C}}$和所有Galois类群元素的子集$\galois{\coring{C}}$上的作用。其中，我们给出了$\coring{C}$是群的条件，使得存在群$\{1\} \to U(A^{g}) \to U(A) \to \galois{\coring{C}} \to \{1\},$的正合序列，其中$A^g$是某个$g \in \galois{\coring{C}}$的共不变量的子代数.
英文摘要：
We focus our attention to the set $\gl{\coring{C}}$ of grouplike elements of a coring $\coring{C}$ over a ring $A$. We do some observations on the actions of the groups $U(A)$ and $\aut{\coring{C}}$ of units of $A$ and of automorphisms of corings of $\coring{C}$, respectively, on $\gl{\coring{C}}$, and on the subset $\galois{\coring{C}}$ of all Galois grouplike elements. Among them, we give conditions on $\coring{C}$ under which $\galois{\coring{C}}$ is a group, in such a way that there is an exact sequence of groups $\{1\} \to U(A^{g}) \to U(A) \to \galois{\coring{C}} \to \{1\},$ where $A^g$ is the subalgebra of coinvariants for some $g \in \galois{\coring{C}}$.
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