加法幂等半环上矩阵的同时幂零性.pdfVIP

() 38 6 Journal of Fujian Agriculture and Forestry Univers ity ( N atural Science Ed ition) 200 11 加法幂等半环上矩阵的同时幂零性 1 2 1 , , ( 1. 福建农林大学计算机与信息学院; 2. 福州大学数学与计算机科学学院, 福建 福州350002) : , . : ; ; : O 151. 21 : A : 1671-5470( 200 ) 06-0668-05 The sim ultaneous nilpotency of m atrices over an additively idempotent sem iring 1 2 1 GUAN M ing-you , TAN Y -i jia, L IDe-xin ( 1. College of Com puter and Inform ation, Fujian Agricu lture and Forestry Un iversity; 2. College of M athematics and Com puter Science, Fuzhou Un iversity, Fuzhou, Fujian 350002, Ch ina) Abstract: The smi ultaneous n ilpotency ofm atrices over an add itively idem potent sem iring w as discussed, and som e necessary and sufficien t conditions form atrices to be smi ultaneously n ilpotent w ere obtained. A canonical form for the smi u ltaneous nilpotency of m atricesw as also given. K ey words: add itively idempotent sem iring; n ilpotent matrix; smi u ltaneous nilpotence . 60, [ 1] , . 1 64G ive n A n [ 2] [ 3] [ 4] A = O. Li . Tan . R en et al [ 5] [ 6] A A 0. Tan Zhang [ 7] . , Han et al . Lur [ 8- ] et al , . , , [ 8- ] . 1 L , / + 0/ # 0L 2. ( 1) (L, + , 0), 0L ; ( 2) (L, #, 1), 1L ; ( 3) a, b, cI L, a ( b+ c) = ab+ ac, (b + c)