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《Journal of Jiangxi Normal University (Natural Sciences Edition)》 2005-04
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Nilpotent Ideals over Hemirings

FENGJian-wen, HUANGFu-sheng(Institute of Mathematics and Informatics ,Jiangxi Normal University,Nanchang 330027 ,China)  
Inthis paper the notion of subtractive ideal and completely subtractive hemiring are intro-duced.Inthe thirdsectionitis provedthatthe definitionof nil ideal over anartin hemiringisinfactequivalent tothe definition of nilpotent ideal . Moreover ,we showthat an artin (noether) hemiringRwhichis completely subtractive has a unique maximal nilpotent idealBsatisfyingthatBcontains allnilpotent one -sidedideals ofRandthe factor hemiringR/ Bdoesn’t have nilpotent ideals .
【Fund】: 江西省自然科学基金资助项目(0211022).
【CateGory Index】: O153.3
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【References】
Chinese Journal Full-text Database 6 Hits
1 FENG Jian-wen1,HUANG Fu-sheng2,ZHOU Yong-zheng1(1.Ceramic-Porclain Institution of Jingdezhen,Jingdezhen Jiangxi 333403;2.Institute of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330022,China);ζ_s-Injective Modules[J];Journal of Jiangxi Normal University(Natural Sciences Edition);2008-03
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【Citations】
Chinese Journal Full-text Database 2 Hits
1 GAN Ai-ping,HUANG Fu-sheng,CHEN Pei-ci(Institute of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330027,China);The Exact Sequences of Semimodules[J];Journal of Jiangxi Normal University (Natural Sciences Edition);2003-02
2 FENG Jian-wen, HUANG Fu-sheng, SHI Ding-qing(Institute of Mathematics and Informatics, Jiangxi Normal University, Jiangxi Nanchang 330027 PRC);The Complemented Semiring[J];Jiangxi Science;2005-03
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 GAN Ai-ping, HUANG Fu-sheng (Institute of Mathematics and Informatics, Jiangxi Normal University, Nanchang 330027,China);The Dual Star Semimodules and the Reflexive Star Semimodules[J];Journal of Jiangxi Normal University (Natural Sciences Edition);2004-06
2 WANG Qi~1,FENG Jian-wen~2,HUANG Fu-sheng~3(1.College of Physics & Communication Electronics,Jiangxi Normal University,Nanchang 330027,China;2.Jingdezhen Ceramic-Porclain Institute,Jingdezhen Jiangxi 333001 China;3.Institute of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330027,China);Injective and Projective Semimodules on Complemented Semirings[J];Journal of Jiangxi Normal University(Natural Sciences Edition);2006-05
3 FENG Jian-wen1,HUANG Fu-sheng2,ZHOU Yong-zheng1(1.Ceramic-Porclain Institution of Jingdezhen,Jingdezhen Jiangxi 333403;2.Institute of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330022,China);ζ_s-Injective Modules[J];Journal of Jiangxi Normal University(Natural Sciences Edition);2008-03
4 XIAO Xian-min,HUANG Fu-sheng,ZENG Hui-ping (Institute of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330022);On the Represent for Functor Hom of Injective Semimodules[J];Journal of Jiangxi Normal University(Natural Sciences Edition);2008-04
5 JIANG Jun,HUANG Fu-sheng (Institute of Mathematics and Informatics,Jiangxi Normal University,NanChang 330022,China);The Decompositions of Well-Semimodules[J];Journal of Jiangxi Normal University(Natural Sciences Edition);2008-04
6 GAN Ai-ping1,HUANG Fu-sheng1,JIANG Yang-lan2,HUANG Wen-ping3 (1.School of Mathematical and Information Sciences,Jiangxi Normal University,Jiangxi 330022,China;2.Jiangxi People's Police College,Jiangxi 330103,China;3.Nanchang Military Academy,Jiangxi 330103,China);Lattice Star Rings and Lattice Star Hemirings[J];Journal of Jiangxi Normal University(Natural Sciences Edition);2008-05
7 QU Cong,WANG Song-sheng,ZHANG wei(Institute of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330027,China);Projective Semimodules[J];Journal of East China Jiaotong University;2006-05
8 CAO Wei-hong~1,HE Xiao-fei~2(1.Xiangxi National Vocational Technical School,Jishou 416000,Hunan China;2.Department of Mathematics and Computer Science,Jishou University,Jishou 416000,Hunan China);Localization of Commutative Semi-Modules[J];Journal of Jishou University(Natural Science Edition);2005-02
9 JIANG Jun,HUANG Fu-sheng,XIAO Xian-min(Institute of Mathematics and Informatics,Jiangxi Normal University,Jiangxi Nanchang 330022 PRC);The Module of Difference of Cancellative Semimodule and it's Homomorphism Extention[J];Jiangxi Science;2007-04
10 NIU Jun-wei,HUANG Fu-sheng(Institute of Mathematics and Informatics,Jiangxi Normal University,Jiangxi Nanchang 330022 PRC);Characterization of Generators of Semimodules[J];Jiangxi Science;2009-04
【Co-references】
Chinese Journal Full-text Database 10 Hits
1 SUN Yongli YU Jianping (Academy of Mathematics and System Sciences,CAS,Beijing,100080) LI Shizheng ZHANG Yufen (Department of Mathematics,Shandong Normal University,Jinan,250014);Congruences on Some Quasi-Completely Regular Semirings[J];Acta Scicentiarum Naturalum Universitis Pekinesis;2004-05
2 GAN Ai-ping,HUANG Fu-sheng,CHEN Pei-ci(Institute of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330027,China);The Exact Sequences of Semimodules[J];Journal of Jiangxi Normal University (Natural Sciences Edition);2003-02
3 GAN Ai-ping, HUANG Fu-sheng (Institute of Mathematics and Informatics, Jiangxi Normal University, Nanchang 330027,China);The Dual Star Semimodules and the Reflexive Star Semimodules[J];Journal of Jiangxi Normal University (Natural Sciences Edition);2004-06
4 AO Zhong-ping1, CHEN Pei-ci2 (1.Dept. of Computer Science ,University of Petroleum(Guangzhou),Guangzhou 510510,China; 2.Institute of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330027,China);Prime-Ideals of -Semirings and Prime-Semirings[J];Journal of Jiangxi Normal University (Natural Sciences Edition);2005-04
5 YANG Wen-qi (Dept.Math, Baoji Coll. Arts and Sci.,Baoji 721007,China);Submaximal ideal of the ring[J];Pure and Applied Mathematics;2003-01
6 OU Qi-tong~1,HUANG Fu-sheng~2,CHEN Pei-ci~2(1.Department of Mathematics and Computer Science,Sanming college,Sanming 365004,China;2.Department of Mathematics,Jiangxi Normal University,Nanchang 330027,China);Star construction of semirings[J];Pure and Applied Mathematics;2006-01
7 OU Qi-tong(Department of Mathematics and Computer Science,Sanming College,Sanming 365004,P R China);Some Properties of Matrix Semiring over a Semiring[J];Journal of Chongqing University(Natural Science Edition);2007-11
8 FENG Ming-jun (Dept.of Math.,Guangdong Education Institute,Guangzhou,Guangdong,510303,P.R.China);The Properties of Weak Ring[J];Journal of Guangdong Education Institute;2005-05
9 OU Qi-tong(Department of Mathematics,Sanming College,Sanming 365004,China);Subdirect Decomposition Theorem of Star Semirings[J];Journal of Gansu Education College(Natural Science Edition);2005-04
10 ZHU Tian-min1,YANG Hui2(1.Department of Mathematics,Shanxi Weinan Teachers College,Shanxi Weinan 714000,China;2.Department of Foundation,Anyang Institute of Technology,Henan Anyang 455001,China);Semilattice Varieties and Multiplicative Band Semirings[J];Journal of Henan University(Natural Science);2007-04
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