论文标题
$ am $ - property的拓扑晶格环
Topological lattice rings with $AM$-property
论文作者
论文摘要
由$ AM $ $ $ property在本地固体矢量晶格中的最新定义[O. Zabeti，Arxiv：1912.00141v2 [Math.fa]]，在本说明中，我们尝试在所有本地实心晶格环的类别中调查这些结果。实际上，我们表征了本地固体晶格环，其中有限的集合和有限集同意。此外，在$ AM $ $ property的帮助下，我们发现了订单有限的群体同态和不同类型的有界组同态的条件。此外，我们表明，当且仅在此类时，只有$ x $，当时每类有界订单有限的组同构$ x $具有Lebegsue或Levi属性。
Motivated by the recent definition of $AM$-property in locally solid vector lattices [O. Zabeti, arXiv: 1912.00141v2 [math.FA]], in this note, we try to investigate those results in the category of all locally solid lattice rings. In fact, we characterize locally solid lattice rings in which order bounded sets and bounded sets agree. Furthermore, with the aid of $AM$-property, we find conditions under that, order bounded group homomorphisms and different types of bounded group homomorphisms coincide. Moreover, we show that each class of bounded order bounded group homomorphisms on a locally solid lattice ring $X$ has the Lebegsue or the Levi property if and only if so is $X$.
