矩形半环的分配格

Distributive lattice of rectangular semirings

借助半群的理论及观点引入并研究了加法半群为矩形群的半环及加法半群为纯正群的半环,即纯正半环和矩形半环.并通过对矩形半环及纯正半环的结构和性质的分析与研究,给出了这两类半环的若干性质,从而给出了矩形半环的分配格的定义.最后研究了矩形半环的分配格与坚固分配格,即对这类半环坚固框架的刻画,得到了一些有趣的新结果.

The concepts of orthodox semirings and rectangular semirlngs were introduced and studied by using the theory and method of semigroup, and then some properties of them were given by analying and studying rectangular sernirings and orthodox semirings, thus the defintion of distributive lattice of rectangular semirings was obtained. Finally some interested results are given by studying the distributive lattice and distributive lattice of the rectangular semiring.