极大代数上有限生成模的凸性  

THE CONVEXITY OF FINITELY GENERATED MODULE OVER MAX-PLUS ALGEBRA

作　　者：霍蕾[1,2] 陶跃钢[1,2] 蔡炳苓[1,2] 张子龙[1,2] 

机构地区：[1]河北师范大学数学与信息科学学院,石家庄050024 [2]河北省计算数学与应用重点实验室,石家庄050024

出　　处：《系统科学与数学》2014年第3期330-339,共10页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(60774007;11271108);河北师范大学青年基金(L2012Q01)资助课题

摘　　要：研究极大代数上有限生成模的凸性.基于极大代数上有限生成模的几何形态,运用代数与几何方法,分析空间维数n≤3和生成向量数m≥1的有限生成模的凸性.证明n=1,2的有限生成模是凸集.对于n=3,给出m=2的有限生成模为凸集的一个充分必要条件,以及m≥3的有限生成模为凸集的一个充分条件.此外,对于极大代数上有限生成模的几何形态,发现n=3,m≥3的形态有三种情形.The convexity of finitely generated module over max-plus algebra is stud- ied in this paper. By applying the geometric shape of finitely generated module and using algebraic method combined with geometric method, the convexity of finitely generated module with dimension n ≤ 3 and the number of generating vector rn ≥ 1 are analyzed. It is proved that the finitely generated module with n = 1, 2 is a convex set. For n = 3, the necessary and sufficient condition for the convexity with m = 2 and the sufficient condition for the convexity with rn ≥ 3 are obtained, respectively. Besides, with regard to the geometric shape of finitely generated module over max-plus algebra, it is found out that there are three types of geometric shapes with n = 3 and rn≥ 3.

关 键 词：极大代数 有限生成模 几何形态 凸性分析 

分 类 号：O174.13[理学—数学]