格群的子积类

Sub-Product Classes of Lattice-Ordered Groups

ｌ－群的一个类称作是子积类，如果它封闭于取凸ｌ－子群及完全次直积。设ｕ是一个子积类，Ｇ是一个ｌ－群。令为Ｇ的直和项且Ｇ／Ｈ∈ｕ｝称作是Ｇ的一个子积根式．我们在本文中证明了一个子积类Ｕ由于积根式映射Ｇ→Ｕ（Ｇ）所决定。我们还证明了在子积类的完备格Ｔ中，一组子积类，由子积根式映射所决定，而并则由子积根式映射所决定．这是一个很漂亮的结果。

A class of l-groups is called a sub-product class,if it is closed under taking convexl-subgroups and forming completely subdirect products.Let U be a sub-product class and G beis called a sub-product radical of G.In this paper we proved that a sub-product class U is determined by the sub-product radical mapping G→U(G).And we also proved that in thethe meet is determined by the sub-product radical mapping G→whilethe join is determined by the sub-product radical mapping G→ this is beautiful result.