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《Journal of Jiangxi Normal University (Natural Sciences Edition)》 2000-04
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Weak Additive Category

CHEN Pei-ci; WANG Quan-long (Institute of Mathematics and Informatics, Jiangxi Normal University, Nanchang 330027, China)  
In this paper, we introduce the concept of a weak additive category based on the category Abs of commutative monoids and the one sM of semimodules and discuss some properties of the coproducts of finite objects in it. Two necssary and sufficient conditions of that a functor of the category to itself reserves finite coproducts are given. Further, we introduce foe concepts of ideals, congruences of a weak additive category and, based on them, prove the fundamental theorem of homomorphisms of a weak additive category and the first (second) isomorphism theorem. Finally, we also discuss the lattice of congruences and subdirect products of weak additive categories. These concepts and results generalized that of additive categories and made a base of researches on the contructure of weak additive categories.
【Fund】: 江西省自然科学基金!(980605)
【CateGory Index】: O154.1
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【Citations】
Chinese Journal Full-text Database 1 Hits
1 Liu Shaoxue (Department of Mathematics);BAER RADICAL AND LEVITZKI RADICAL OF ADDITIVE CATEGORIES[J];Journal of Beijing Normal University(Natural Science);1987-04
【Co-citations】
Chinese Journal Full-text Database 10 Hits
1 OU Qi-tong,DENG Huo-di(Department of Mathematics and Computer Science,Sanming College,Sanming 365004,China);Bi-ideal of semiring[J];Journal of University of Science and Technology Liaoning;2009-03
2 Chen Peici(Dept. of Math. of Jiangxi Normal University,Nanchang 330027);Homomorphic Theorems of the Semirings with Reversible Addition[J];Journal of Jiangxi Normal University (Natural Sciences Edition);1994-02
3 AO Zhong-ping(Department of Computer Science,Guangzhou Petroleum,Guangzhou 510510,China);On a New Describition of J-Semisimple Semirings[J];Journal of Jiangxi Normal University (Natural Sciences Edition);2003-01
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 ZHANG Ting-hai,CHEN Pei-ci,HUANG Fu-sheng(Institute of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330027,China);-Structure of Semimodule[J];Journal of Jiangxi Normal University(Natural Sciences Edition);2006-03
6 AO Zhong-ping1,CHEN Pei-ci2,CAI Shu-ping1 (1.Department of Computer Science,Universityof Petroleum,Guangzhou,510510,China;2.Institute of Mathematics and Information,Jiangxi Normal University,Nanchang,330027,China);Exact Sequence of Cancellable Semimodules[J];Journal of Jiangxi Normal University(Natural Sciences Edition);2008-06
7 AO Zhong-Ping 1,CHEN Pei-ci2,CAI Shu-ping1 (1.Department of Computer Science,Guangzhou University of Petroleum,Guangzhou 510510,China;2.Institute of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330022,China);Semireal Semiring Based on Being Subtractive and Semireal Prime Ideals[J];Journal of Jiangxi Normal University(Natural Sciences Edition);2009-05
8 GAN Ai-ping1,JIANG Yang-lan2,HUANG Fu-sheng1(1.College of Mathematics and Informatics,Jiangxi Normal University,Nanchang Jiangxi 330022,China;2.Jiangxi People's Police College,Nanchang Jiangxi 330103,China);L-Star Semirings[J];Journal of Jiangxi Normal University(Natural Science Edition);2010-02
9 QIN Song,GAN Ai-ping(College of Mathematics and Informatics,Jiangxi Normal University,Nanchang Jiangxi 330022,China);The Green's Relations on a Semiring with Additive Semigroup as Semilattice[J];Journal of Jiangxi Normal University(Natural Science Edition);2012-02
10 Chen Peici (Department of Mathematics,Jiangxi Normal University,Nanchang 330027);The f regular Radicals of the Semirings with Reversible Addition[J];JOURNAL OF JIANGXI NORMAL UNIVERSITY (NATURAL SCIENCES EDITION);1997-01
【Secondary Citations】
Chinese Journal Full-text Database 1 Hits
1 Liu Shaoxue (Department of Mathematics);BAER RADICAL AND LEVITZKI RADICAL OF ADDITIVE CATEGORIES[J];Journal of Beijing Normal University(Natural Science);1987-04
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