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《Journal of Jiangxi Normal University(Natural Sciences Edition)》 1993-03
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The Strong Ideal of Semiring and Prime-semiring

Ao Zhongping (Dept.of Math.)  
In this paper,we introduced the concept of the strong ideal in a semiring whose additional semirings are groups,the ideal of a semiring in the class and its congruenee are the only determinant to each other.So,it is feasible to make quotient by ideal of a semir- ing.On basis of it,the concepts of prime-semirngs and semiprime-semirings are established and some algebraic properties of theirs are discussed in the paper.
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【References】
Chinese Journal Full-text Database 8 Hits
1 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
2 AO Zhong-ping1,CHEN Pei-ci2,SONG Hai-yan1(1.Department of Computer Science,University of Petroleum,Guangzhou 510510,China;2.Institute of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330027,China);The Orders of Semirings and Semireal Semirings[J];Journal of Jiangxi Normal University(Natural Sciences Edition);2007-02
3 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
4 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
5 Zhou Yuanlan (Department of Mathematics of Jiangxi Normal Uinversity,Nanchang 330027);Superprime Properties of the Semirings with Reversible Addition[J];JOURNAL OF JIANGXI NORMAL UNIVERSITY (NATURAL SCIENCES EDITION);1998-04
6 AO Zhong-ping 1,CHEN Pei-ci 2,XIAO Lie-hong 3(1.Department of Computer Science,University of Petroleum(Guangzhou),Guangzhou 510510,China;2.Department of Mathematics,Jiangxi Normal University,Nanchang 330027,China;3.Department of Mathematics and Physics,School of Biomedical Engineering of Southern Medical University,Guangzhou 510515,China);Real semiring based on being subtractive and real prime ideals[J];Pure and Applied Mathematics;2010-03
7 Zhang Tinghai & Guo Jing(Jiangxi Normal University, Nanchang 330027, China; Jiangxi Science & Technology Normal University, Nanchang 330013, China);The Popularization of the Nature of Semi-ring Absorbable Element[J];Journal of Jiangxi Science & Technology Teahers' College;2004-06
8 AO Zhongping,CAI Shuping,SONG Haiyan (Department of Computer Science,University of Petroleum(Guangzhou),Guangzhou Guangdong 510510);Five Lemma of Cancellable Semimodules[J];Journal of Xinjiang Normal University(Natural Sciences Edition);2008-02
【Co-references】
Chinese Journal Full-text Database 10 Hits
1 Cheu Peici;Superprime Rings and Superspecial Radicals[J];Journal of Jiangxi Normal University(Natural Sciences Edition);1988-01
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 AO Zhong-ping1,CHEN Pei-ci2,SONG Hai-yan1(1.Department of Computer Science,University of Petroleum,Guangzhou 510510,China;2.Institute of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330027,China);The Orders of Semirings and Semireal Semirings[J];Journal of Jiangxi Normal University(Natural Sciences Edition);2007-02
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 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
9 ZHANG Juan-juan1,SHAO Yong2,LI Yi-peng3(1.Department of Mathematics,Northwest University,Xi'an 710069,China;2.College of Science,Xi'an Polytechnic University,Xi'an 710048,China;3.College of Science,Xi'an University of Science and Technology,Xi'an 710054,China);The Structure of the Members in Some Quasivarieties of Idempotent Semirings[J];Journal of Nanchang University(Natural Science);2009-01
10 CHEN Pei Ci, ZHOU Yuan Lan (Department of Mathematics, Jiangxi Normal University, Nanchang 330027 , P. R. China ) ( E-mail: chenpeic@jxnu.cn);Tensor Product of Semimodules[J];Acta Mathematica Sinica;2002-01
【Secondary References】
Chinese Journal Full-text Database 10 Hits
1 AO Zhong-ping1,CHEN Pei-ci2,SONG Hai-yan1(1.Department of Computer Science,University of Petroleum,Guangzhou 510510,China;2.Institute of Mathematics and Informatics,Jiangxi Normal University,Nanchang 330027,China);The Orders of Semirings and Semireal Semirings[J];Journal of Jiangxi Normal University(Natural Sciences Edition);2007-02
2 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
3 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
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5 AO Zhong-ping 1,CHEN Pei-ci 2,XIAO Lie-hong 3(1.Department of Computer Science,University of Petroleum(Guangzhou),Guangzhou 510510,China;2.Department of Mathematics,Jiangxi Normal University,Nanchang 330027,China;3.Department of Mathematics and Physics,School of Biomedical Engineering of Southern Medical University,Guangzhou 510515,China);Real semiring based on being subtractive and real prime ideals[J];Pure and Applied Mathematics;2010-03
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9 OU Qi-tong(Department of Mathematics and Computer Science,Sanming College,Sanming 365004,China);Submaximal Ideal of Semiring[J];Journal of Guangxi University for Nationalities(Natural Science Edition);2008-03
10 LIU Xing,HUANG Fu-sheng(College of Mathematics and Informatics,Jiangxi Normal University,Nanchang Jiangxi 330022,China);The Completely Subtractive Injective Decomposition of Cancellative Semimodule[J];Journal of Jiangxi Normal University(Natural Science Edition);2012-05
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