论文标题
有限维矢量空间的子空间的晶格中的正交性和互补
Orthogonality and complementation in the lattice of subspaces of a finite-dimensional vector space over a finite field
论文作者
论文摘要
我们研究了有限场GF（Q）上M维矢量空间V的子空间的晶格L（V），Q是prime p的第n个功率。众所周知，该晶格是模块化的，正交性是抗蛋白的反应。晶格L（V）满足链条条件，我们确定其元素的覆盖量，尤其是其原子的数量。我们表征何时正交性是一种互补性，因此何时l（v）是矫正的。对于M> 1，M不容易被P排除，我们表明L（V）包含某个（非树状）正数晶格作为子店。最后，对于q是素数，M = 2，我们通过简单的条件表征L（V）的正数。
We investigate the lattice L(V) of subspaces of an m-dimensional vector space V over a finite field GF(q) with q being the n-th power of a prime p. It is well-known that this lattice is modular and that orthogonality is an antitone involution. The lattice L(V) satisfies the Chain condition and we determine the number of covers of its elements, especially the number of its atoms. We characterize when orthogonality is a complementation and hence when L(V) is orthomodular. For m > 1 and m not divisible by p we show that L(V) contains a certain (non-Boolean) orthomodular lattice as a subposet. Finally, for q being a prime and m = 2 we characterize orthomodularity of L(V) by a simple condition.
